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CBSE Class 10 Maths Case Study Questions for Maths Chapter 6 (Published by CBSE)

Check case study questions released by cbse for class 10 maths chapter 6 - triangles. solve these questions to prepare the case study questions for the cbse class 10 maths exam 2021-22..

CBSE Class 10 Maths Case Study Questions for Chapter 6 - Triangles are available here. Students must practice with these questions to perform well in their Maths exam. All these case study questions have been published by the Central Board of Secondary Education (CBSE). For the convenience of students, all the questions are provided with answers.

Case Study Questions for Class 10 Maths Chapter 6 - Triangles

CASE STUDY 1:

Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles.The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground.

1. What is the height of the tower?

Answer: c) 100m

2. What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?

Answer: d) 60m

3. What is the height of Ajay’s house?

Answer: b) 40m

4. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house?

Answer: a) 16m

5. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijay’s house?

Answer: d) 8m

CASE STUDY 2:

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below. To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12m, connecting C to point D at a distance of 40m from point C and the connecting D to the point A which is are a distance of 30m from D such the ∠ ADC=90 0 .

1. Which property of geometry will be used to find the distance AC?

a) Similarity of triangles

b) Thales Theorem

c) Pythagoras Theorem

d) Area of similar triangles

Answer: c)Pythagoras Theorem

2. What is the distance AC?

Answer: a) 50m

3. Which is the following does not form a Pythagoras triplet?

a) (7, 24, 25)

b) (15, 8, 17)

c) (5, 12, 13)

d) (21, 20, 28)

Answer: d) (21, 20, 28)

4. Find the length AB?

Answer: b) 38m

5. Find the length of the rope used.

Answer: c)82m

SCALE FACTOR

Case study:

A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor

Scale factor= length in image / corresponding length in object

If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200

This means that a length of 1 cm on the photograph above corresponds to a length of 200cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths.

1. If the length of the model is 11cm, then the overall length of the engine in the photograph above, including the couplings (mechanism used to connect) is:

Answer: a)22m

2. What will affect the similarity of any two polygons?

a) They are flipped horizontally

b) They are dilated by a scale factor

c) They are translated down

d) They are not the mirror image of one another.

Answer: d)They are not the mirror image of one another

3. What is the actual width of the door if the width of the door in photograph is 0.35cm?

Answer: a)0.7m

4. If two similar triangles have a scale factor 5:3 which statement regarding the two triangles is true?

a) The ratio of their perimeters is 15:1

b) Their altitudes have a ratio 25:15

c) Their medians have a ratio 10:4

d) Their angle bisectors have a ratio 11:5

Answer: b)Their altitudes have a ratio 25:15

5. The length of AB in the given figure:

Answer: c)4cm

Also Check:

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Case Study Questions for Class 10 Maths Chapter 6 Triangles

Last modified on: 10 months ago
Reading Time: 4 Minutes

Case Study Questions:

Question 1:

Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay’s house if 20 m when Vijay’s house casts a shadow 10 m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20 m shadow on the ground.

(i) What is the height of the tower? (a) 20 m (b) 50 m (c) 100 m (d) 200 m

(ii) What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m? (a) 75 m (b) 50 m (c) 45 m (d) 60 m

(iii) What is the height of Ajay’s house? (a) 30 m (b) 40 m (c) 50 m (d) 20 m

(iv) When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house? (a) 16 m (b) 32 m (c) 20 m (d) 8 m

(v) When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijay’s house? (a) 15 m (b) 32 m (c) 16 m (d) 8 m

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Class 10 Maths Chapter 6 Case Based Questions - Triangles

Case study - 1.

Case Study - 2

Q1: What is the height of the tower? (a) 20m (b) 50m (c) 100m (d) 200m Ans: (c) Explanation: The properties of similar triangles state that the ratios of the corresponding sides of the triangles are equal. Hence the ratio of the height of Vijay's house to the length of its shadow equals to the ratio of the height of the tower to the length of its shadow. Therefore, the height of the tower can be calculated as follows: Height of the tower = (Height of Vijay's house / Length of Vijay's house's shadow) * Length of the tower's shadow = (20m / 10m) * 50m = 100m Q2: What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m? (a) 75m (b) 50m (c) 45m (d) 60m Ans: (d) Explanation: Applying the same method, we can find the length of the shadow of the tower. Length of the tower's shadow = (Length of Vijay's house's shadow / Height of Vijay's house) * Height of the tower = (12m / 20m) * 100m = 60m Q3: What is the height of Ajay’s house? (a) 30m (b) 40m (c) 50m (d) 20m Ans: (b) Explanation: Similarly, the height of Ajay's house can be calculated as follows: Height of Ajay's house = (Height of Vijay's house / Length of Vijay's house's shadow) * Length of Ajay's house's shadow = (20m / 10m) * 20m = 40m Q4: When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house? (a) 16m (b) 32m (c) 20m (d) 8m Ans: (a) Explanation: Length of Ajay's house's shadow = (Length of the tower's shadow / Height of the tower) * Height of Ajay's house = (40m / 100m) * 40m = 16m Q5: When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijay’s house? (a) 15m (b) 32m (c) 16m (d) 8m Ans: (d) Explanation: Length of Vijay's house's shadow = (Length of the tower's shadow / Height of the tower) * Height of Vijay's house = (40m / 100m) * 20m = 8m

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CBSE Case Study Questions for Class 10 Maths Triangles Free PDF

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CBSE Case Study Questions for Class 10 Maths Triangles PDF

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Class 10th Maths - Triangles Case Study Questions and Answers 2022 - 2023

By QB365 on 09 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 10th Maths Subject - Triangles, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

QB365 - Question Bank Software

Triangles case study questions with answer key.

10th Standard CBSE

Final Semester - June 2015

(ii) If m, n and r are the sides of right triangle ABJ, then which of the following can be correct?

(iii) If $\Delta$ ABJ ~ $\Delta$ ADH, then which similarity criterion is used here?

(iv) If $\angle$ ABJ = 90° and B, J are mid points of sides AD and AH respectively and BJ || DH, then which of the following option is false?

(ii) Distance travelled by aeroplane towards west after $1 \frac{1}{2}$ hr is

(iii) In the given figure, $\angle$ POQ is

(iv) Distance between aeroplanes after $1 \frac{1}{2}$ hr is

(v) Area of $\Delta$ POQ is

(ii) Which criterion of similarity is applied here?

(iii) Height of the building is

(iv) In $\Delta$ ABM, if LBAM = 30°, then LMCD is equal to

(v) If $\Delta$ ABM and $\Delta$ CDMare similar where CD = 6 ern, MD = 8 cm and BM = 24 ern, then AB is equal to

(ii) What will be the length of shadow of tower when Meenal's house casts a shadow of 15 m?

(iii) Height of Aruns house is

(iv) If tower casts a shadow of 40 rn, then find the length of shadow of Arun's house

(v) If tower casts a shadow of 40 m, then what will be the length of shadow of Meenal's house?

(ii) The length of CD is

(iii) Area of whole empty land is

(iv) Area of $\Delta$ PAB is

(v) Area of $\Delta$ PCD is

(ii) The value of x is

(iii) The value of PR is

(iv) The value of RQ is

(v) How much distance will be saved in reaching city Q after the construction of highway?

(ii) In if AB || CD, and DO = 3x - 19, OB = x - 5, OC = x - 3 and AO = 3, then the value of x can be

(iii) In if OD = 3x - 1, OB = 5x - 3, OC = 2x + 1 and AO = 6x - 5, then the value of x is

(iv) In $\Delta$ ABC, if PQ || BC and AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, then AB + PQ is equal to

(v) In $\Delta$ DEF, if RS || EF, DR = 4x - 3, DS = 8x - 7, ER = 3x - 1 and FS = 5x - 3, then the value of x is

(ii) Length of BC =

(iii) Length of AD =

(iv) Length of ED =

(v) Length of AE =

(ii) If the distance between Aruna and the bus is twice as much as the height of the bus, then the height of the bus is

(iii) If the distance of Aruna from the building is twelve times the height of the bus, then the ratio of the heights of bus and building is

(iv) What is the ratio of the distance between Aruna and top of bus to the distance between the tops of bus and building?

(v). What is the height of the building?

(ii) The distance between the hotel A and hut-I is

(iii) If the horizontal distance between the hut -1 and hut -2 is 8 miles, then the distance between the two hotels is

(iv) If the distance from mountain top to hut-1 is 5 miles more than that of distance from hotel B to mountain top, then what is the distance between hut-2 and mountain top?

(v) What is the ratio of areas of two parts formed in the complete figure?

(b) What is the length of string pulled in 12 seconds?

(d) What will be the horizontal distance of the fly from her after 12 seconds?

(e) The given problem is based on which concept?

(ii) What is the distance AC?

(iii) Which is the following does not form a Pythagoras triplet?

(iv) Find the length AB.

(v) Find the length of the rope used.

(ii) Which is the correct similarity criteria applicable for smaller triangles at the upper part of this kite?

(iii) Sides of two similar triangles are in the ratio 4:9. Corresponding medians of these triangles are in the ratio,

(iv) In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This theorem is called as,

(v) What is the area of the kite, formed by two perpendicular sticks of length 6 cm and 8 cm?

(ii) Find the correct similarity criteria applicable for triangles ABE and CDE.

(iii) Find the length of her shadow after 4 seconds.

(iv) Sides of two similar triangles are in the ratio 9:16. Find the ratio of Corresponding areas of these triangles.

(v) Find the ratio AC:CE.

(ii) State the criterion of similarity, that will be used in the above found triangles.

(iii) What is the height of the tree?

(iv) What is the distance between Rashmi and Gulmohar tree?

*****************************************

Triangles case study questions with answer key answer keys.

(i) (a): Speed = 1200 km/hr $\text { Time }=1 \frac{1}{2} \mathrm{hr}=\frac{3}{2} \mathrm{hr}$ $\therefore$ Required distance = Speed x Time $=1200 \times \frac{3}{2}=1800 \mathrm{~km}$ (ii) (c): Speed = 1500 km/hr Time = $\frac{3}{2}$ hr. $\therefore$ Required distance = Speed x Time $=1500 \times \frac{3}{2}=2250 \mathrm{~km}$ (iii) (b): Clearly, directions are always perpendicular to each other. $\therefore \quad \angle P O Q=90^{\circ}$ (iv) (a): Distance between aeroplanes after $1\frac{1}{2}$ hour $\begin{array}{l} =\sqrt{(1800)^{2}+(2250)^{2}}=\sqrt{3240000+5062500} \\ =\sqrt{8302500}=450 \sqrt{41} \mathrm{~km} \end{array}$ (v) (d): Area of $\Delta$ POQ= $\frac{1}{2}$ x base x height $=\frac{1}{2} \times 2250 \times 1800=2250 \times 900=2025000 \mathrm{~km}^{2}$

(i) (c): Since, $\angle$ B = $\angle$ D = 90°, $\angle$ AMB = $\angle$ CMD ( $\because$ Angle of incident = Angle of reflection) $\therefore$ By similarity criterion, $\Delta$ ABM $\sim$ $\Delta$ CDM (ii) (a) (iii) (c) : $\because$ $\Delta$ ABM $\sim$ $\Delta$ CDM $\begin{array}{l} \therefore \quad \frac{A B}{C D}=\frac{B M}{D M} \Rightarrow \frac{A B}{1.8}=\frac{2.5}{1.5} \\ \Rightarrow \quad A B=\frac{2.5 \times 1.8}{1.5}=3 \mathrm{~m} \end{array}$ (iv) (b): Since $\Delta$ ABM $\sim$ $\Delta$ CDM $\because$ $\angle$ A= $\angle$ C=30° [ $\therefore$ Corresponding angles of similar triangles are also equal] (v) (b): Since $\Delta$ ABM $\sim$ $\Delta$ CDM $\therefore \frac{A B}{C D}=\frac{B M}{M D} \Rightarrow \quad \frac{A B}{6}=\frac{24}{8} \Rightarrow A B=18 \mathrm{~cm}$

(i) (a): In $\Delta$ PAB and $\Delta$ PQR, $\angle$ P = $\angle$ P (Common) $\angle$ A = $\angle$ Q (Corresponding angles) By AA similarity criterion, $\Delta$ PAB $\sim$ $\Delta$ PQR $\therefore \frac{A B}{Q R}=\frac{P A}{P Q} \Rightarrow \frac{A B}{12}=\frac{6}{24} \Rightarrow A B-3 \mathrm{~m}$ (ii) (d): Similarly, $\Delta$ PCD and $\Delta$ PQR are similar $\therefore \frac{P C}{P Q}=\frac{C D}{Q R} \Rightarrow \frac{14}{24}=\frac{C D}{12} \Rightarrow C D=7 \mathrm{~m}$ (iii) (a): Area of whole empty land = $\frac{1}{2}$ x base x height = $\frac{1}{2}$ x 1 x15= 90 m 2 . (iv) (b): Since, $\Delta$ PAB $\sim$ $\Delta$ PQR $\therefore \frac{\operatorname{ar}(\Delta P A B)}{a r(\Delta P Q R)}=\left(\frac{P A}{P Q}\right)^{2}=\left(\frac{6}{24}\right)^{2}=\frac{1}{16}$ $\Rightarrow \quad \operatorname{ar}(\Delta P A B)=\frac{1}{16} \times 90=\frac{45}{8} \mathrm{~m}^{2}$ $\left[\because \operatorname{ar}(\Delta P Q R)=90 \mathrm{~m}^{2}\right]$ (v) (d): Since, $\Delta$ PCD $\sim$ $\Delta$ PQR $\therefore \frac{\operatorname{ar}(\Delta P C D)}{\operatorname{ar}(\Delta P Q R)}=\left(\frac{P C}{P Q}\right)^{2}=\left(\frac{14}{24}\right)^{2}=\left(\frac{7}{12}\right)^{2}$ $\Rightarrow \operatorname{ar}(\Delta P C D)=\frac{90 \times 49}{144}=\frac{245}{8} \mathrm{~m}^{2}$

(i) (b) (ii) (c): Using Pythagoras theorem, we have PQ 2 = PR 2 + RQ 2 $\Rightarrow(26)^{2}=(2 x)^{2}+(2(x+7))^{2} \Rightarrow 676=4 x^{2}+4(x+7)^{2} $ $\Rightarrow 169=x^{2}+x^{2}+49+14 x \Rightarrow x^{2}+7 x-60=0$ $\Rightarrow x^{2}+12 x-5 x-60=0 $ $\Rightarrow x(x+12)-5(x+12)=0 \Rightarrow(x-5)(x+12)=0 $ $\Rightarrow x=5, x=-12$ $\therefore \quad x=5$ [Since length can't be negative] (iii) (a) : PR = 2x = 2 x 5 = 10 km (iv) (b): RQ= 2(x + 7) = 2(5 + 7) = 24 km (v) (d): Since, PR + RQ = 10 + 24 = 34 km Saved distance = 34 - 26 = 8 km

(i) (c) (ii) (b): Since $\Delta$ AOB ~ $\Delta$ COD [ByAA similarity criterion] $\therefore \frac{A O}{O C}=\frac{B O}{O D} \Rightarrow \frac{3}{x-3}=\frac{x-5}{3 x-19}$ $\Rightarrow 3(3 x-19)=(x-5)(x-3) $ $\Rightarrow 9 x-57=x^{2}-3 x-5 x+15 \Rightarrow x^{2}-17 x+72=0 $ $\Rightarrow(x-8)(x-9)=0 \Rightarrow x=8 \text { or } 9$ (iii) (c) : Since, $\Delta$ AOB ~ $\Delta$ COD [ByAA similarity criterion] $\therefore \frac{A O}{O C}=\frac{B O}{O D} \Rightarrow \frac{6 x-5}{2 x+1}=\frac{5 x-3}{3 x-1}$ $\Rightarrow(6 x-5)(3 x=1)=(5 x-3)(2 x+1) $ $\Rightarrow \quad 18 x^{2}-6 x-15 x+5=10 x^{2}+5 x-6 x-3 $ $\Rightarrow \quad 8 x^{2}-20 x+8=0 \Rightarrow 2 x^{2}-5 x+2=0$ From options, x = 2 is the only value that satisfies this equation. (iv) (d): Since, $\Delta$ APQ ~ $\Delta$ ABC [ByAA similarity criterion] $\therefore \quad \frac{A P^{\circ}}{A B}=\frac{A Q}{A C}=\frac{P Q}{B C} \Rightarrow \frac{2.4}{A B}=\frac{2}{5}=\frac{P Q}{6} $ $\therefore \quad A B=\frac{2.4 \times 5}{2}=6 \mathrm{~cm} \text { and } P Q=\frac{2 \times 6}{5}=2.4 \mathrm{~cm} $ $\therefore \quad A B+P Q=6+2.4=8.4 \mathrm{~cm}$ (v) (a): Since, $\Delta$ DRS ~ $\Delta$ DEF [ByAA similarity criterion] $\therefore \quad \frac{D E}{D R}=\frac{D F}{D S} \Rightarrow \frac{D E}{D R}-1=\frac{D F}{D S}-1 $ $\Rightarrow \frac{D E-D R}{D R}=\frac{D F-D S}{D S} \Rightarrow \frac{E R}{D R}=\frac{F S}{D S} $ $\Rightarrow \quad \frac{D R}{E R}=\frac{D S}{F S} \Rightarrow \frac{4 x-3}{3 x-1}=\frac{8 x-7}{5 x-3} $ $\Rightarrow \quad 20 x^{2}-12 x-15 x+9=24 x^{2}-8 x-21 x+7 $ $\Rightarrow \quad 4 x^{2}-2 x-2=0 \Rightarrow 2 x^{2}-x-1=0$ Only option (a) i.e., x = 1 satisfies this equation.

(i) (b): If $\Delta$ AED and $\Delta$ BEC, are similar by SAS similarity rule, then their corresponding proportional sides are $\frac{B E}{A E}=\frac{C E}{D E}$ (ii) (c): By Pythagoras theorem, we have $\begin{array}{l} B C=\sqrt{C E^{2}+E B^{2}}=\sqrt{4^{2}+3^{2}}=\sqrt{16+9} \\ =\sqrt{25}=5 \mathrm{~cm} \end{array}$ (iii) (a): Since $\Delta$ ADE and $\Delta$ BCE are similar. $\therefore \quad \frac{\text { Perimeter of } \triangle A D E}{\text { Perimeter of } \Delta B C E}=\frac{A D}{B C} $ $\Rightarrow \frac{2}{3}=\frac{A D}{5} \Rightarrow A D=\frac{5 \times 2}{3}=\frac{10}{3} \mathrm{~cm}$ (iv) (b): $\frac{\text { Perimeter of } \triangle A D E}{\text { Perimeter of } \Delta B C E}=\frac{E D}{C E} $ $\Rightarrow \frac{2}{3}=\frac{E D}{4} \Rightarrow E D=\frac{4 \times 2}{3}=\frac{8}{3} \mathrm{~cm}$ (v) (d) : $\frac{\text { Perimeter of } \Delta A D E}{\text { Perimeter of } \Delta B C E}=\frac{A E}{B E} \Rightarrow \frac{2}{3} B E=A E$ $\Rightarrow A E=\frac{2}{3} \sqrt{B C^{2}-C E^{2}} $ $\text { Also, in } \triangle A E D, A E=\sqrt{A D^{2}-D E^{2}}$

(i) (b): AC 2 = AB 2 + BC 2 [ By Pythagoras theorem ] ⇒ AC 2 = (1.8)2 + (2.4) 2 ⇒ AC 2 = 3.24 + 5.76 ⇒ AC 2 = 9 ⇒ AC = 3m (ii) (c): She pulls the string at the rate of 5cm/s ∴ String pulled in 12 second = 12 x 5 = 60cm = 0.6 (iii) (a): Length of string out after 12 second is AP. ⇒ AP = AC – String pulled by Nazima in 12 seconds. ⇒ AP = (3 − 0.6)m = 2.4m (iv) (b): In △ADB, AB 2 + BP 2 = AP 2 ⇒ (1.8)2 + BP 2 = (2.4) 2 ⇒ BP 2 = 5.76 − 3.24 ⇒ BP 2 = 5.76 − 3.24 ⇒ BP 2 = 2.52 ⇒ BP = 1.58 m Horizontal distance of fly = BP + 1.2m Horizontal distance of fly =1.58m + 1.2m ∴ Horizontal distance of fly = 2.78m (v) (a): Triangles

(i) (c): Pythagoras Theorem (ii) (a): ADC is a right-angled triangle. By Pythagoras theorem we get AC 2 = (30) 2 + (40) 2 ⇒ AC 2 = 900 + 1600 ⇒ AC 2 = 2500 ⇒ AC = 50m (iii) (d): (21, 20, 28) since, $(28)^{2} \neq(20)^{2}+(21)^{2}$ (iv) (b): AC = 50m and BC = 12m ⇒ AB = AC - BC ⇒ AB = 50 - 12 = 38m (v) (c): Length of the rope used = 30 + 40 + 12 = 82m

(i) (c): In this kite shape, diagonals bisect each other at 90 o . (ii) (b): SAS (iii) (b): Since ratio of sides of similar triangles = Ratio of their corresponding medians Therefore, the required ratio is 4 : 9. (iv) (d): Converse of Pythagoras theorem (v) (c): Since ,length sticks are 6 cm and 8 cm or length of diagonals Then, Area of kite $=\frac{1}{2} \times d_{1} \times d_{2}$ $=\frac{6 \times 8}{2}$ = 24 cm 2

(i) (c): Let AB denote the lamp-post and CD the girl after walking for 4 seconds away from the lamp-post. From the figure, DE is the shadow of the girl. Let DE be x metres. Now, her distance from the base of the lamp = BD = 1.2 m x 4 = 4.8 m. (ii) (a): In $\triangle$ ABE and $\triangle$ CDE, $\angle$ B = $\angle$ D ( Each is of 90 o ) and $\angle$ E = $\angle$ E (same angle) So, $\Delta \mathrm{ABE} \sim \Delta \mathrm{CDE}$ (AA similarity criterion) (iii) (d): $\Delta \mathrm{ABE} \sim \Delta \mathrm{CDE}$ $\Rightarrow \frac{\mathrm{BE}}{\mathrm{DE}}=\frac{\mathrm{AB}}{\mathrm{CD}}$ $\Rightarrow \frac{4.8+x}{x}=\frac{3.6}{0.9} \quad \Rightarrow 4.8+x=4 x$ $\Rightarrow 3 x=4.8 \ \Rightarrow \ x=1.6$ So, the shadow of the girl after walking for 4 seconds is 1.6 m long. (iv) (b): Since ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides, Ratio of areas of similar triangles = $\sqrt{9}$ : $\sqrt{16}$ = 3 : 4 (v) (b): $\frac{A E}{C E}=\frac{B E}{D E}=\frac{4.8+1.6}{1.6}=\frac{6.4}{1.6}=4$ $\Rightarrow$ AE = 4 CE $\Rightarrow$ AC + CE = 4 CE $\Rightarrow A C=3 C E \Rightarrow \frac{A C}{C E}=\frac{3}{1}$

(i) (b): (b) $\triangle$ s PQM and RSM (ii) (d): AA similarity As $\angle \mathrm{PQM}=\angle \mathrm{RSM}=90^{\circ}$ and angle of incidence is equal to angle of reflection. Then, $\angle \mathrm{PMQ}=\angle \mathrm{RMS}$ (iii) (a): Since, $\Delta \mathrm{PMQ} \sim \Delta \mathrm{RMS}$ Then, $\frac{\mathrm{PQ}}{\mathrm{RS}}=\frac{\mathrm{QM}}{\mathrm{MS}} \Rightarrow \mathrm{PQ}=\frac{2.8 \times 2}{1.4}$ = 4m (iv) (c): Distance between Rashmi and Gulmohar tree QS = QM + MS = 2.8 + 1.4 = 4.2 m

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Question 5 - Case Based Questions (MCQ) - Chapter 6 Class 10 Triangles

Last updated at April 16, 2024 by Teachoo

An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour.

This question is inspired from Ex 6.5, 11 - Chapter 6 Class 10 - Triangles

What is the distance travelled by aeroplane towards north after 11/2 hours?

(a) 1000 , (c) 1500 .

What is the distance travelled by aeroplane towards west after 11/2 hours?

∠ AOB is

(a) 90° , (b) 45° , (c) 30° , (d) 60°.

How far apart will the two planes be after 1 1/2 hours?

(a) √22,50,000 , (b) √32,40,000, (c) √54,90,000 , (d) none of these.

Chapter 6 Triangles - Class 10- Case Based Questions.jpg

The given problem is based on which concept?

(a) triangles, (b) co-ordinate geometry, (c) height and distance.

Question An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. We know that Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒 Distance = Speed × Time Thus, OA = 1500 km & OB = 1800 km Question 1 What is the distance travelled by aeroplane towards north after 11/2 hours? (a) 1000 (b) 1200 (c) 1500 (d) 1800 Distance travelled towards north = OA = 1500 km So, the correct answer is (c) Question 2 What is the distance travelled by aeroplane towards west after 11/2 hours? (a) 1000 (b) 1200 (c) 1500 (d) 1800 Distance travelled towards north = OB = 1800 km So, the correct answer is (d) Question 3 ∠ AOB is (a) 90° (b) 45° (c) 30° (d) 60° Since North is always perpendicular to West Hence, ∠AOB = 90° So, the correct answer is (c) Question 4 How far apart will the two planes be after 1 1/2 hours? (a) √22,50,000 (b) √32,40,000 (c) √54,90,000 (d) none of these Distance between two planes after 1 1/2 hours = AB In right angled Δ AOB By Pythagoras Theorem AB2 = OA2 + OB2 AB2 = (1500)2 + (1800)2 AB2 = 22,50,000 + 32,40,000 AB2 = 54,90,000 + 32,40,000 AB = √𝟓𝟒𝟗𝟎𝟎𝟎𝟎 km So, the correct answer is (c) Question 5 The given problem is based on which concept? (a) Triangles (b) Co-ordinate geometry (c) Height and Distance (d) none of these Since this question involves Pythagoras Theorem Which is in Triangles Class 10 So, the correct answer is (a)

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Class 10 Maths
Chapter 6: Triangles

Important questions Class 10 Maths Chapter 6 - Triangles

Important questions for Class 10 Maths Chapter 6 Triangles are provided here to help the students in their exam preparation based on the new pattern of CBSE for the 2022-2023 academic session. Students preparing for the board exam are advised to practice these important Triangles questions to score full marks for the questions from this chapter. In the exam, students may come across some of these questions. So, they should not leave any stone unturned for their board exam and must practice these questions. They can also access important questions for 10th maths all chapters at BYJU’S.

The chapter Triangles contains many topics related to a triangle, such as criteria for similarity, congruency, areas of similar triangles and the Pythagoras theorem etc., Students can also get the answers to all the questions in Class 10 Maths of NCERT solutions .

Triangles For Class 10
Types of Triangles
Area Of Similar Triangles

We have provided important questions of this chapter, along with the detailed solutions. After that, we have also provided some questions for students to practice which does not have solutions, and they must solve all of them to gain command over the Triangles topic.

Important Questions & Answers For Class 10 Maths Chapter 6 Triangles

Q. 1: In the given figure, PS/SQ = PT/TR and ∠ PST = ∠ PRQ. Prove that PQR is an isosceles triangle.

PS/SQ = PT/TR

We know that if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Therefore, ST // QR

And ∠ PST = ∠ PQR (Corresponding angles) ……..(i)

Also, given,

∠ PST = ∠ PRQ………(ii)

From (i) and (ii),

∠ PRQ = ∠ PQR

Therefore, PQ = PR (sides opposite the equal angles)

Hence, PQR is an isosceles triangle.

Q. 2: In the figure, DE // AC and DF // AE. Prove that BF/FE = BE/EC.

Given that,

In triangle ABC, DE // AC.

By Basic Proportionality Theorem,

BD/DA = BE/EC……….(i)

Also, given that DF // AE.

Again by Basic Proportionality Theorem,

BD/DA = BF/FE……….(ii)

BE/EC = BF/FE

Hence proved.

Q. 3: In the given figure, altitudes AD and CE of ∆ ABC intersect each other at the point P. Show that:

(i) ∆AEP ~ ∆ CDP

(ii) ∆ABD ~ ∆ CBE

(iii) ∆AEP ~ ∆ADB

(iv) ∆ PDC ~ ∆ BEC

Given that AD and CE are the altitudes of triangle ABC and these altitudes intersect each other at P.

(i) In ΔAEP and ΔCDP,

∠AEP = ∠CDP (90° each)

∠APE = ∠CPD (Vertically opposite angles)

Hence, by AA similarity criterion,

ΔAEP ~ ΔCDP

(ii) In ΔABD and ΔCBE,

∠ADB = ∠CEB ( 90° each)

∠ABD = ∠CBE (Common Angles)

ΔABD ~ ΔCBE

(iii) In ΔAEP and ΔADB,

∠AEP = ∠ADB (90° each)

∠PAE = ∠DAB (Common Angles)

ΔAEP ~ ΔADB

(iv) In ΔPDC and ΔBEC,

∠PDC = ∠BEC (90° each)

∠PCD = ∠BCE (Common angles)

ΔPDC ~ ΔBEC

Q. 4: A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower

Length of the vertical pole = 6 m

Shadow of the pole = 4 m

Let the height of the tower be h m.

Length of the shadow of the tower = 28 m

In ΔABC and ΔDFE,

∠C = ∠E (angle of elevation)

∠B = ∠F = 90°

By AA similarity criterion,

ΔABC ~ ΔDFE

We know that the corresponding sides of two similar triangles are proportional.

AB/DF = BC/EF

h = (6 ×28)/4

Hence, the height of the tower = 42 m.

Q. 5: If ΔABC ~ ΔQRP, ar (ΔABC) / ar (ΔPQR) =9/4 , AB = 18 cm and BC = 15 cm, then find PR.

Given that ΔABC ~ ΔQRP.

ar (ΔABC) / ar (ΔQRP) =9/4

AB = 18 cm and BC = 15 cm

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

ar (ΔABC) / ar (ΔQRP) = BC 2 /RP 2

9/4 = (15) 2 /RP 2

RP 2 = (4/9) × 225

Therefore, PR = 10 cm

Q. 6: If the areas of two similar triangles are equal, prove that they are congruent.

Let ΔABC and ΔPQR be the two similar triangles with equal area.

To prove ΔABC ≅ ΔPQR.

ΔABC ~ ΔPQR

Q. 7: O is any point inside a rectangle ABCD as shown in the figure. Prove that OB 2 + OD 2 = OA 2 + OC 2 .

Through O, draw PQ || BC so that P lies on AB and Q lies on DC.

Therefore, PQ ⊥ AB and PQ ⊥ DC (∠ B = 90° and ∠ C = 90°)

So, ∠ BPQ = 90° and ∠ CQP = 90°

Hence, BPQC and APQD are both rectangles.

By Pythagoras theorem,

OB 2 = BP 2 + OP 2 …..(1)

OD 2 = OQ 2 + DQ 2 …..(2)

OC 2 = OQ 2 + CQ 2 …..(3)

OA 2 = AP 2 + OP 2 …..(4)

Adding (1) and (2),

OB 2 + OD 2 = BP 2 + OP 2 + OQ 2 + DQ 2

= CQ 2 + OP 2 + OQ 2 + AP 2

(since BP = CQ and DQ = AP)

= CQ 2 + OQ 2 + OP 2 + AP 2

Hence proved that OB 2 + OD 2 = OA 2 + OC 2 .

Q. 8: Sides of triangles are given below. Determine which of them are right triangles.

In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

(i) Given, sides of the triangle are 7 cm, 24 cm, and 25 cm.

Squaring the lengths of the sides of the, we will get 49, 576, and 625.

49 + 576 = 625

(7) 2 + (24) 2 = (25) 2

Therefore, the above equation satisfies the Pythagoras theorem. Hence, it is a right-angled triangle.

Length of Hypotenuse = 25 cm

(ii) Given, sides of the triangle are 3 cm, 8 cm, and 6 cm.

Squaring the lengths of these sides, we will get 9, 64, and 36.

Clearly, 9 + 36 ≠ 64

Or, 3 2 + 6 2 ≠ 8 2

Therefore, the sum of the squares of the lengths of two sides is not equal to the square of the length of the hypotenuse.

Hence, the given triangle does not satisfy the Pythagoras theorem.

Q.9: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

Consider a triangle ΔABCand draw a line PQ parallel to the side BC of ΔABC and intersect the sides AB and AC in P and Q, respectively.

To prove: AP/PB = AQ/QC

Cosntruction:

Join the vertex B of ΔABC to Q and the vertex C to P to form the lines BQ and CP and then drop a perpendicular QN to the side AB and draw PM⊥AC as shown in the given figure.

Now the area of ∆APQ = 1/2 × AP × QN (Since, area of a triangle= 1/2× Base × Height)

Similarly, area of ∆PBQ= 1/2 × PB × QN

area of ∆APQ = 1/2 × AQ × PM

Also,area of ∆QCP = 1/2 × QC × PM ………… (1)

Now, if we find the ratio of the area of triangles ∆APQand ∆PBQ, we have

According to the property of triangles, the triangles drawn between the same parallel lines and on the same base have equal areas.

Therefore, we can say that ∆PBQ and QCP have the same area.

area of ∆PBQ = area of ∆QCP …………..(3)

Therefore, from the equations (1), (2) and (3), we can say that,

AP/PB = AQ/QC

Q.10: In the figure, DE || BC. Find the length of side AD, given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm.

AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm

By basic proportionality theorem,

AD/DB = AE/EC

AD/7.2 = 1.8/5.4

AD = (1.8 × 7.2)/5.4

Therefore, AD = 2.4 cm.

Q.11: Given ΔABC ~ ΔPQR, if AB/PQ = ⅓, then find (ar ΔABC)/(ar ΔPQR).

AB/PQ = ⅓,

We know that The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

(ar ΔABC)/(ar ΔPQR) = AB 2 /PQ 2 = (AB/PQ) 2 = (⅓) 2 = 1/9

Therefore, (ar ΔABC)/(ar ΔPQR) = 1/9

(ar ΔABC) : (ar ΔPQR) = 1 : 9

Q.12: The sides of two similar triangles are in the ratio 7 : 10. Find the ratio of areas of these triangles.

The ratio of sides of two similar triangles = 7 : 10

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

The ratio of areas of these triangles = (Ratio of sides of two similar triangles) 2

= (7) 2 : (10) 2

Therefore, the ratio of areas of the given similar triangles is 49 : 100.

Q.13: In an equilateral ΔABC, D is a point on side BC such that BD = (⅓) BC. Prove that 9(AD) 2 = 7(AB) 2 .

Given, ABC is an equilateral triangle.

And D is a point on side BC such that BD = (1/3)BC.

Let a be the side of the equilateral triangle and AE be the altitude of ΔABC.

∴ BE = EC = BC/2 = a/2

And, AE = a√3/2

Given, BD = 1/3BC

DE = BE – BD = a/2 – a/3 = a/6

In ΔADE, by Pythagoras theorem,

AD 2 = AE 2 + DE 2

= [(a√3)/2] 2 + (a/6) 2

= (3a 2 /4) + (a 2 /36)

= (37a 2 + a 2 )/36

= (28a 2 )/36

= (7/9) (AB) 2

Therefore, 9(AD) 2 = 7(AB) 2 .

Q.14: Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given: A right-angled triangle ABC, right-angled at B.

To Prove: AC 2 = AB 2 + BC 2

Construction: Draw a perpendicular BD meeting AC at D.

In ΔABC and ΔADB,

∠ABC = ∠ADB = 90°

∠A = ∠A → common

Using the AA criterion for the similarity of triangles,

ΔABC ~ ΔADB

Therefore, AD/AB = AB/AC

⇒ AB 2 = AC x AD ……(1)

Considering ΔABC and ΔBDC from the figure.

C = ∠C → common

∠CDB = ∠ABC = 90°

Using the Angle Angle(AA) criterion for the similarity of triangles, we conclude that,

ΔBDC ~ ΔABC

Therefore, CD/BC = BC/AC

⇒ BC 2 = AC x CD …..(2)

By adding equation (1) and equation (2), we get:

AB 2 + BC 2 = (AC x AD) + (AC x CD)

AB 2 + BC 2 = AC (AD + CD) …..(3)

AB 2 + BC 2 = AC (AC) {since AD + CD = AC}

AB 2 + BC 2 = AC 2

Q.15: In the figure, if PQ || RS, prove that ∆ POQ ~ ∆ SOR.

∠P = ∠S (Alternate angles)

and ∠Q = ∠R

Also, ∠POQ = ∠SOR (Vertically opposite angles)

Therefore, ∆ POQ ~ ∆ SOR (by AAA similarity criterion)

Video Lesson on BPT and Similar Triangles

Class 10 Maths Chapter 6 Triangles Questions for Practice

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP.
Diagonals of a trapezium PQRS intersect each other at the point O, PQ || RS and PQ = 3RS. Find the ratio of the areas of triangles POQ and ROS.
Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle is 48 cm 2 , find the area of the larger triangle.
A foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.
An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1 1/2 hours?
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that OA/OC = OB/OD.
Prove that if in a triangle square on one side is equal to the sum of the squares on the other two sides, then the angle opposite the first side is a right angle.

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CBSE Class 10 Maths Syllabus

Real Numbers
Polynomials
Pair of Linear Equations in Two Variables
Quadratic Equations
Arithmetic Progressions
Coordinate Geometry
Probability
Introduction to Trigonometry
Some Applications of Trigonometry
Constructions
Area Related to Circles
Surface Areas and Volumes

UNIT I: NUMBER SYSTEMS

1. REAL NUMBER

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality.

UNIT II: ALGEBRA

POLYNOMIALS Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.
QUADRATIC EQUATIONS Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.
ARITHMETIC PROGRESSIONS Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

UNIT III: COORDINATE GEOMETRY Coordinate Geometry Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

UNIT IV: GEOMETRY

TRIANGLES Definitions, examples, counter examples of similar triangles. 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3.(Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 4.(Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. 5.(Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
CIRCLES Tangent to a circle at, point of contact 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2.(Prove) The lengths of tangents drawn from an external point to a circle are equal.

UNIT V: TRIGONOMETRY

INTRODUCTION TO TRIGONOMETRY Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0° and 90°. Values of the trigonometric ratios of 30°, 45°, and 60°. Relationships between the ratios.
TRIGONOMETRIC IDENTITIES Proof and applications of the identity sin2A + cos2A = 1 . Only simple identities to be given.
HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression. (10)Periods Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.

UNIT VI: MENSURATION

AREAS RELATED TO CIRCLES Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.
SURFACE AREAS AND VOLUMES Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

UNIT VII: STATISTICS AND PROBABILITY

STATISTICS Mean, median and mode of grouped data (bimodal situation to be avoided).
PROBABILITY (10) Periods Classical definition of probability. Simple problems on finding the probability of an event.

PRESCRIBED BOOKS:

Mathematics - Textbook for class IX - NCERT Publication
Mathematics - Textbook for class X - NCERT Publication
Guidelines for Mathematics Laboratory in Schools, class IX - CBSE Publication
Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication
Laboratory Manual - Mathematics, secondary stage - NCERT Publication
Mathematics exemplar problems for class IX, NCERT publication.
Mathematics exemplar problems for class X, NCERT publication.

Structure of CBSE Maths Sample Paper for Class 10 is

For Preparation of board exams students can also check out other resource material

CBSE Class 10 Maths Sample Papers

Important Questions for Class 10 Maths Chapter Wise

Maths Revision Notes for class 10

Previous Year Question Paper CBSE Class 10 Maths

Worksheets of Other Subjects of Class 10

Why do one Children need Worksheets for Practice ?

It is very old saying that one can build a large building if the foundation is strong and sturdy. This holds true for studies also. Worksheets are essential and help students in the in-depth understanding of fundamental concepts. Practicing solving a lot of worksheets, solving numerous types of questions on each topic holds the key for success. Once basic concepts and fundamentals have been learnt, the next thing is to learn their applications by practicing problems. Practicing the problems helps us immensely to gauge how well we have understood the concepts.

There are times when students just run through any particular topic with casual awareness there by missing out on a few imperative “between the lines” concepts. Such things are the major causes of weak fundamental understandings of students. So in such cases Worksheets act as a boon and critical helpful tool which gauges the in-depth understanding of children highlighting doubts and misconceptions, if any.

Worksheets classifies the important aspects of any topic or chapter taught in the class in a very easy manner and increases the awareness amongst students.When students try to solve a worksheet they get to understand what are the key important factors which needs the main focus.Sometimes it happens that due to shortage of time all the major points of any particular topic gets skipped in the class or teacher rushes through , due to shortage of time. A worksheet thus provides a framework for the entire chapter and can help covering those important aspects which were rushed in the class and ensure that students record and understand all key items.

In a class of its say 40 students howsoever teacher tries to be active and work towards making each student understand whatever she has to teach in the class but there are always some students who tend to be in their own world and they wander in their thoughts.Worksheets which are provided timely to all the students, causes them to focus on the material at hand. it’s simply the difference between passive and active learning. Worksheets of this type can be used to introduce new material, particularly material with many new definitions and terms.

Worksheets help students be focussed and attentive in the class because they know after the class is over they will be assigned a worksheet which they need to solve so if they miss or skip any point in the class they may not be able to solve the worksheet completely and thereby lose reputation in the class.

Often students revise the chapter at home reading their respective textbooks. Thus more often than not they do miss many important points. Worksheets thus can be used intentionally to help guide student’s to consult textbooks. Having students write out responses encourages their engagement with the textbooks, the questions chosen indicate areas on which to focus. Explicitly discussing the worksheets and why particular questions are asked helps students reflect on what is important.

Worksheets of Other Classes

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Class 10 Case Study Questions with Answers - Triangles

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Case Study Chapter 6 Triangles Mathematics

Refer to Case Study Chapter 6 Triangles Mathematics, these class 10 maths case study based questions have been designed as per the latest examination guidelines issued for the current academic year by CBSE, NCERT, KVS. Students should go through these solves case studies so that they are able to understand the pattern of questions expected in exams and get good marks.

Chapter 6 Triangles Mathematics Case Study Based Questions

I. Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles.The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground.

Question. What is the height of Ajay’s house? (a) 30m (b) 40m (c) 50m (d) 20m

Question. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijay’s house? (a) 15m (b) 32m (c) 16m (d) 8m

Question. What is the height of the tower? (a) 20m (b) 50m (c) 100m (d) 200m

Question. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house? (a) 16m (b) 32m (c) 20m (d) 8m

Question. What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m? (a) 75m (b) 50m (c) 45m (d) 60m

l. Read the following and answer Two trees are standing parallel to each other. The bigger tree 8 m high, casts a shadow of 6 m.

Case Study Chapter 6 Triangles Mathematics

Question. If the ratio of the height of two trees is 3 : 1, then the shadow of the smaller tree is (a) 2 m (b) 6 m (c) 8/3 m (d) 8 m

Question. If , ΔABC ∼ ΔPQR , ar (ΔABC)/ ar (ΔPQR) = 4/25 , PQ = 10 cm, then AB is equal to (a) 4 cm (b) 2 cm (c) 5 cm (d) 5 8 cm

Question. If AB and CD are the two trees and AE is the shadow of the longer tree, then (a) ΔAEB ∼ ΔCED (b) ΔABE ∼ ΔCED (c) ΔAEB ∼ ΔDEC (d) ΔBEA ∼ ΔDEC

Question. Since AB ll CD , so by basic proportionality theorem, we have (a) AE/CE = BD/DE (b) AC/AE = DE/BE (c) AE/CE = AB/CD (d) AE/CE = BE/DE

Question. The distance of point B from E is (a) 10 m (b) 8 m (c) 18 m (d) 10/3 m

ll. Read the following and answer A ladder was placed against a wall such that it touches a point 4 m above the ground. The distance of the foot of the ladder from the bottom of the ground was 3 m. Keeping its foot at the same point, Akshay turns the ladder to the opposite side so that it reached the window of his house.

Question. In an isosceles right triangle PQR, right angled at P, then (a) QR 2 = 2PQ 2 (b) QP 2 = 2PR 2 (c) QP 2 = 2QR 2 (d) PR 2 = 2QR 2

Question. If OA 2 = OB 2 + AB 2 , then (a) ΔOBA is an equilateral triangle. (b) ΔOAB is an isosceles right triangle. (c) ΔOAB is a right triangle right angled at O. (d) ΔOAB is a right triangle right angled at B.

Question. The theorem which can be used for find the length of the ladder is (a) Thales Theorem (b) Converse of Thales Theorem (c) Pythagoras Theorem (d) Converse of Pythagoras Theorem

Question. The length of the ladder, in metre is (a) 4 m (b) 5 m (c) 9 m (d) 2 m

Question. If the window of the house is 3 m above the ground, then the distance of the point C from D is (a) 3 m (b) 4 m (c) 5 m (d) 3.5 m

lll. Read the following and answer Two buildings (say A and B) are located 12 m apart. The height of the two buildings are 32 m and 41 m.

Question. The distance DF is equal to (a) 15 m (b) 12 m (c) 9 m (d) 21 m

Question. In a triangle PQR, PQ = 7 cm, QR = 25 cm, RP = 24 cm, then the triangle is right angled at (a) P (b) Q (c) R (d) can’t say

Question. ABC is an equilateral triangle of side ‘2a’ units. The length of each of its altitude is (a) a units (b) 2a units (c) √2 a units (d) √3 a units

Question. The distance between the top of the two buildings can be calculated using (a) Thales Theorem (b) Pythagoras Theorem (c) Converse of Thales Theorem (d) Converse of Pythagoras Theorem

Question. The length EF in the figure is (a) 32 m (b) 41 m (c) 41 m/2 (d) 9 m

lV. Read the following and answer A farmer had a triangular piece of land. He put a fence, parallel to one of the sides of the field as shown in the figure.

Question. If AD = x + 1, DB = 3x – 1, AE = x + 3, EC = 3x + 4, then (a) x = 5 (b) x = 7 (c) x = 8 (d) x = 4

Question. If the point D is 20 m away from A, where as AB and AC are 80 m and 100 m respectively, then (a) AE = 20 m (b) EC = 25 cm (c) AE = 25 cm (d) EC = 60 cm

Question. Which of the following is not true? (a) AD/AB = AE/AC (b) AD/AE = AB/AC (c) AB/BD = AC/EC (d) BD/AD = AE/EC

Question. Which of the following statements is true? (a) AD/DB = AE/EC , using Thales Theorem (b) AD/DB = AE/EC , using Pythagoras Theorem (c) AD/DB = AE/EC , using Pythagoras Theorem (d) AD/DB = AE/EC , using Thales Theorem

Question. If P and Q are the mid points of sides YZ and XZ respectively, then (a) PQ ll XY (b) PQ ll YZ (c) PQ ll ZX (d) None of these

V. Read the following and answer The ratio of two corresponding sides in similar figures is called scale factor. Scale factor = Length of image / Actual length of object

Question. Two similar triangles have a scale factor of 1 : 2. Then their corresponding altitudes have a ratio (a) 2 : 1 (b) 4 : 1 (c) 1 : 2 (d) 1 : 1

Question. If two similar triangles have a scale factor of 2 : 5, then which of the following statements is true ? (a) The ratio of their medians is 2 : 5. (b) The ratio of their altitudes is 5 : 2. (c) The ratio of their perimeters is 2 × 3 : 5. (d) The ratio of their altitudes is 22 : 52.

Question. The shadow of a statue 8 m long has length 5 m. At the same time the shadow of a pole 5.6 m high is (a) 3 m (b) 3.5 m (c) 4 cm (d) 4.5 m

Question. For two similar polygons which of the following is not true? (a) They are not flipped horizontally. (b) They are dilated by a scale factor. (c) They cannot be translated down. (d) They are mirror images of each other.

Question. A model of a car is made on the scale 1 : 8. The model is 40 cm long and 20 cm wide. The actual length of car is (a) 320 cm (b) 160 cm (c) 5 cm (d) 2.5 cm

Worksheets for class 10 mathematics surface area and volume, worksheets for class 10 japanese, worksheets for class 10 social science economics.

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Case Study Class 10...

Case Study Class 10 Maths Questions

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Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

Real Numbers Case Study Question
Polynomials Case Study Question
Pair of Linear Equations in Two Variables Case Study Question
Quadratic Equations Case Study Question
Arithmetic Progressions Case Study Question
Triangles Case Study Question
Coordinate Geometry Case Study Question
Introduction to Trigonometry Case Study Question
Some Applications of Trigonometry Case Study Question
Circles Case Study Question
Area Related to Circles Case Study Question
Surface Areas and Volumes Case Study Question
Statistics Case Study Question
Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

Find the production in the 1 st year.
Find the production in the 12 th year.
Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

Find the distance between Lucknow (L) to Bhuj(B).
If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

Find the distance PA.
Find the distance PB
Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

What is the length of the line segment joining points B and F?
The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

If the first circular row has 30 seats, how many seats will be there in the 10th row?
For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

$case study questions triangles class 10$

Draw a neat labelled figure to show the above situation diagrammatically.

$case study questions triangles class 10$

What is the speed of the plane in km/hr.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

CBSE Class 10 Maths Sample Paper 2020-21
Class 12 Maths Case Study Questions
CBSE Reduced Syllabus Class 10 (2020-21)
Class 10 Maths Basic Sample Paper 2024
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Case Study Class 10 Maths

If you are looking for the CBSE Case Study class 10 Maths in PDF, then you are in the right place. CBSE 10th Class Case Study for the Maths Subject is available here on this website. These Case studies can help the students to solve the different types of questions that are based on the case study or passage.

CBSE Board will be asking case study questions based on Maths subjects in the upcoming board exams. Thus, it becomes an essential resource to study.

The Case Study Class 10 Maths Questions cover a wide range of chapters from the subject. Students willing to score good marks in their board exams can use it to practice questions during the exam preparation. The questions are highly interactive and it allows students to use their thoughts and skills to solve the given Case study questions.

Download Class 10 Maths Case Study Questions and Answers PDF (Passage Based)

Download links of class 10 Maths Case Study questions and answers pdf is given on this website. Students can download them for free of cost because it is going to help them to practice a variety of questions from the exam perspective.

Case Study questions class 10 Maths include all chapters wise questions. A few passages are given in the case study PDF of Maths. Students can download them to read and solve the relevant questions that are given in the passage.

Students are advised to access Case Study questions class 10 Maths CBSE chapter wise PDF and learn how to easily solve questions. For gaining the basic knowledge students can refer to the NCERT Class 10th Textbooks. After gaining the basic information students can easily solve the Case Study class 10 Maths questions.

Case Study Questions Class 10 Maths Chapter 1 Real Numbers

Case Study Questions Class 10 Maths Chapter 2 Polynomials

Case Study Questions Class 10 Maths Chapter 3 Pair of Equations in Two Variables

Case Study Questions Class 10 Maths Chapter 4 Quadratic Equations

Case Study Questions Class 10 Maths Chapter 5 Arithmetic Progressions

Case Study Questions Class 10 Maths Chapter 6 Triangles

Case Study Questions Class 10 Maths Chapter 7 Coordinate Geometry

Case Study Questions Class 10 Maths Chapter 8. Introduction to Trigonometry

Case Study Questions Class 10 Maths Chapter 9 Some Applications of Trigonometry

Case Study Questions Class 10 Maths Chapter 10 Circles

Case Study Questions Class 10 Maths Chapter 12 Areas Related to Circles

Case Study Questions Class 10 Maths Chapter 13 Surface Areas & Volumes

Case Study Questions Class 10 Maths Chapter 14 Statistics

Case Study Questions Class 10 Maths Chapter 15 Probability

How to Solve Case Study Based Questions Class 10 Maths?

In order to solve the Case Study Based Questions Class 10 Maths students are needed to observe or analyse the given information or data. Students willing to solve Case Study Based Questions are required to read the passage carefully and then solve them.

While solving the class 10 Maths Case Study questions, the ideal way is to highlight the key information or given data. Because, later it will ease them to write the final answers.

Case Study class 10 Maths consists of 4 to 5 questions that should be answered in MCQ manner. While answering the MCQs of Case Study, students are required to read the paragraph as they can get some clue in between related to the topics discussed.

Also, before solving the Case study type questions it is ideal to use the CBSE Syllabus to brush up the previous learnings.

Features Of Class 10 Maths Case Study Questions And Answers Pdf

Students referring to the Class 10 Maths Case Study Questions And Answers Pdf from Selfstudys will find these features:-

Accurate answers of all the Case-based questions given in the PDF.
Case Study class 10 Maths solutions are prepared by subject experts referring to the CBSE Syllabus of class 10.
Free to download in Portable Document Format (PDF) so that students can study without having access to the internet.

Benefits of Using CBSE Class 10 Maths Case Study Questions and Answers

Since, CBSE Class 10 Maths Case Study Questions and Answers are prepared by our maths experts referring to the CBSE Class 10 Syllabus, it provided benefits in various way:-

Case study class 10 maths helps in exam preparation since, CBSE Class 10 Question Papers contain case-based questions.
It allows students to utilise their learning to solve real life problems.
Solving case study questions class 10 maths helps students in developing their observation skills.
Those students who solve Case Study Class 10 Maths on a regular basis become extremely good at answering normal formula based maths questions.
By using class 10 Maths Case Study questions and answers pdf, students focus more on Selfstudys instead of wasting their valuable time.
With the help of given solutions students learn to solve all Case Study questions class 10 Maths CBSE chapter wise pdf regardless of its difficulty level.

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Class 10 Maths Case Study Questions Chapter 6 Triangles PDF Download
Triangles
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CBSE Class 10 Maths Case Study Questions for Maths Chapter 6 Triangles

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TRIANGLES CLASS 10 (LECTURE 1) ONE SHOT IMPORTANT QUESTIONS TRIANGLES EXAMINATION BOARDS NCERT
TRIANGLES CLASS 10 (LECTURE 3) ONE SHOT IMPORTANT QUESTIONS TRIANGLES EXAMINATION BOARDS NCERT
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Class 10 Triangles ( Exercise 2.1, All problems solved)
Triangles Class 10
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CBSE Class 10 Case Study Questions for Maths Chapter 6 Triangles
For the convenience of students, all the questions are provided with answers. Case Study Questions for Class 10 Maths Chapter 6 - Triangles. CASE STUDY 1: Vijay is trying to find the average ...
CBSE 10th Standard Maths Triangles Case Study Questions With Solution
CBSE 10th Standard Maths Subject Triangles Case Study Questions With Solution 2021. An aeroplane leaves an airport and flies due north at a speed of 1200km /hr. At the same time, another aeroplane leaves the same station and flies due west at the speed of 1500 km/hr as shown below. After \ (1 \frac {1} {2}\) hr both the aeroplanes reaches at ...
CBSE Class 10 Maths: Case Study Questions of Chapter 6 Triangles PDF
Triangles Case Study Questions With answers. Here, we have provided case-based/passage-based questions for Class 10 Maths Chapter 6 Triangles. Case Study/Passage-Based Questions. Question 1: Meenal was trying to find the height of the tower near his house. She is using the properties of similar triangles. The height of Meenal's house is 20 m.
Case Study Questions for Class 10 Maths Chapter 6 Triangles
Case Study Questions: Question 1: Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay's house if 20 m when Vijay's house casts a shadow 10 m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts ...
Case Study on Triangles Class 10 Maths PDF
Students looking for Case Study on Triangles Class 10 Maths can use this page to download the PDF file. The case study questions on Triangles are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Triangles case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 Maths ...
Class 10 Maths Case Study Questions Chapter 6 Triangles PDF Download
Triangles Case Study Questions With Answers. Here, we have provided case-based/passage-based questions for Class 10 Maths Chapter 6 Triangles. Case Study/Passage-Based Questions. Case Study 1: Meenal was trying to find the height of the tower near his house. She is using the properties of similar triangles. The height of Meenal's house is 20 m.
Class 10 Maths
This video explains the detailed solution and explanation of Case Study Based Questions related to Chapter 6 Triangles which include the concepts of Similar ... CBSE Exam, class 10
CBSE Class 10 Maths Triangles Case Study Questions
Triangles Case Study Questions (CSQ's) Practice Tests. Timed Tests. Select the number of questions for the test: Select the number of questions for the test: TopperLearning provides a complete collection of case studies for CBSE Class 10 Maths Triangles chapter. Improve your understanding of biological concepts and develop problem-solving ...
Class 10 Maths Chapter 6 Case Based Questions
The Case Based Questions: Triangles is an invaluable resource that delves deep into the core of the Class 10 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
CBSE Case Study Questions for Class 10 Maths Triangles Free PDF
Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Triangles in order to fully complete your preparation.They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!. I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams.
Class 10th Maths
By QB365 on 09 Sep, 2022 . QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 10th Maths Subject - Triangles, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles
NCERT Solutions Class 10 Maths Chapter 6, Triangles, is part of the Unit Geometry, which constitutes 15 marks of the total marks of 80. On the basis of the updated CBSE Class 10 Syllabus for 2023-24, this chapter belongs to the Unit-Geometry and has the second-highest weightage. Hence, having a clear understanding of the concepts, theorems and ...
Chapter 6 Class 10 Triangles
Updated for new NCERT 2023-2024 Edition. Get NCERT Solutions of Chapter 6 Class 10 Triangles free at teachoo. Solutions to all NCERT Exercise Questions, Examples, Theorems, Optional Exercises are available with Videos of each and every question. We have studied Congruency of Triangles in Class 9. In this chapter, we will learn. What are Similar ...
Case Based Question
Question 5 - Case Based Questions (MCQ) - Chapter 6 Class 10 Triangles Last updated at April 16, 2024 by ... none of these Since this question involves Pythagoras Theorem Which is in Triangles Class 10 So, the correct answer is (a) Show More. Next: NCERT Exemplar - MCQ → Go Ad-free Chapter 6 Class 10 Triangles; Serial order wise;
Important questions for Class 10 Maths Chapter 6 Triangles
Class 10 Maths Chapter 6 Triangles Questions for Practice. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP.
CBSE(NCERT) Maths Class X Chapter 06 Triangles Case Study ...
CBSE(NCERT) Maths Class X Chapter 06 Triangles Case Study Based Questions (First Round)Please share the link with all Class X Student:https://youtu.be/s4Fkjj...
CBSE Class 10 Maths Case Study Questions PDF
These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards. CBSE Class 10 Mathematics Exam 2024 will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in ...
Class 10 Case Study Questions with Answers
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 4.
Case Study Chapter 6 Triangles Mathematics
Refer to Case Study Chapter 6 Triangles Mathematics, these class 10 maths case study based questions have been designed as per the latest examination guidelines issued for the current academic year by CBSE, NCERT, KVS. Students should go through these solves case studies so that they are able to understand the pattern of questions expected in exams and get good marks.
CBSE Class 10 Maths Case Study : Case Study With Solutions
CBSE Board has introduced the case study questions for the ongoing academic session 2021-22. The board will ask the paper on the basis of a different exam pattern which has been introduced this year where 50% syllabus is occupied for MCQ for Term 1 exam. Selfstudys has provided below the chapter-wise questions for CBSE Class 10 Maths.
Case Study Class 10 Maths Questions
First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.
Case Study Class 10 Maths Questions and Answers (Download PDF)
Students referring to the Class 10 Maths Case Study Questions And Answers Pdf from Selfstudys will find these features:-. Accurate answers of all the Case-based questions given in the PDF. Case Study class 10 Maths solutions are prepared by subject experts referring to the CBSE Syllabus of class 10. Free to download in Portable Document Format ...