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Take a guided, problem-solving based approach to learning Geometry. These compilations provide unique perspectives and applications you won't find anywhere else.

Geometry Fundamentals

What's inside.

• Introduction
• Angles and Lengths
• Pythagoras' Geometry
• Scaling and Volume
• When Geometry Gets Tough

Beautiful Geometry

• Tessellations and Reptiles
• Folding Puzzles
• Guarding Galleries
• Pick's Theorem
• Composite Polygons
• Regular Polygons

Community Wiki

Browse through thousands of Geometry wikis written by our community of experts.

Geometric Measurement

• Parallel Lines (Geometry)
• Area of a Triangle
• Area of a Rectangle
• Length and Area Problem Solving
• Composite Figures
• Volume of a Cuboid
• Volume of a Cylinder
• Volume of a Sphere
• Volume of a Pyramid
• Volume Problem Solving
• Calculating the Size of Earth
• Sphere Packing
• Surface Area
• Surface Area of a Cuboid
• Surface Area of a Sphere
• Surface Area of a Cylinder
• Pythagorean Theorem
• Triangle Inequality
• Classification of Triangles
• Properties of Equilateral Triangles
• Properties of Isosceles Triangles
• Congruent and Similar Triangles
• Heron's Formula
• Pascal's Theorem
• Centroid of a Triangle
• Circumcenter
• Orthocenter
• Ceva's Theorem
• Apollonius's Theorem
• Quadrilateral Classification
• Properties of Squares
• Properties of Rectangles
• Properties of Parallelograms
• Properties of Trapezoids (US) / Trapeziums (UK)
• Similar Figures
• Basic Composite Figures
• Irregular Polygons
• Area of a Polygon
• Tangent - Perpendicular to Radius
• Alternate Segment Theorem
• Two Secants
• Tangent-Secant
• Incircle of Triangle
• Incircles and Excircles
• Cyclic Quadrilaterals
• Steiner Ellipse, Minimal Area Through Three Points

Coordinate Geometry

• Linear Equations
• Equations of Parallel and Perpendicular Lines
• Midpoint of a Line Segment
• Distance Formula
• Distance between Point and Line
• Section Formula
• Equation of Locus
• Determining Coordinates
• Coordinate Geometry - Angle Bisector
• Conic Sections
• Equation of a Circle
• Discriminant of a Conic Section
• 3D Coordinate Geometry - Distance
• 3D Coordinate Geometry - Equation of a Line
• 3D Coordinate Geometry - Skew Lines
• 3D Coordinate Geometry - Equation of a Plane
• 3D Coordinate Geometry - Parallel Planes
• 3D Coordinate Geometry - Perpendicular Planes
• 3D Coordinate Geometry - Intersection of Planes
• Trigonometry
• Converting Degrees and Radians
• Basic Trigonometric Functions
• Reciprocal Trigonometric Functions
• Inverse Trigonometric Functions
• Bearing - Word Problems
• Hyperbolic Trigonometric Functions
• Local Linearization
• Sine and Cosine Graphs
• Tangent and Cotangent Graphs
• Cosecant and Secant Graphs
• Inverse Trigonometric Graphs
• Symmetry in Trigonometric Graphs
• Trigonometric Graphs - Amplitude and Periodicity
• Graphical Transformation of Trigonometric Functions
• Graphs of Trigonometric Functions - Problem Solving
• Trigonometric Equations
• Trigonometric Equations - Double Angle Formula
• Lengths in Right Triangles
• Sine Rule (Law of Sines)
• Cosine Rule (Law of Cosines)
• Solving Triangles

Trigonometric Identities

• Pythagorean Identities
• Ratio of Trigonometric Functions
• Trigonometric Even-odd Functions
• Trigonometric Periodicity Identities
• Trigonometric Co-function Identities
• Trigonometric R method
• Fundamental Trigonometric Identities - Problem Solving (Easy)
• Double Angle Identities
• Sum and Difference Formulas
• Triple Angle Identities
• Expansions of sin(nx) and cos(nx)
• Half Angle Tangent Substitution
• Trigonometric Power Reduction Identities
• Product-to-Sum Trigonometric Formulas
• Sum to Product Trigonometric Identities
• Proving Trigonometric Identities
• Chebyshev Polynomials - Definition and Properties
• Vector Addition
• Vector Decomposition
• Unit Vectors
• Dot Product
• Cross Product

3D Geometry

• Regular Polyhedra

Euclidean Geometry

• Isosceles Triangle Theorem
• Angle Bisector Theorem
• Menelaus' Theorem
• Stewart's Theorem
• Orthic Triangle
• Nine-point Circle
• Routh's Theorem
• Pedal Triangle
• Projective Geometry
• Brahmagupta's Formula
• Power of a Point
• Radical Axis of 2 Circles
• Ptolemy's Theorem
• Pitot's Theorem
• Descartes' Circle Theorem

Geometric Transformations

• Affine transformations
• Does 1 square meter equal 100 square centimeters?
• Can a triangle have an angle of 0 degrees?
• Möbius Strips
• Klein Bottle
• Spherical Geometry
• Hyperbolic Geometry
• Metric Space
• Homeomorphism
• Stone-Weierstrass Theorem
• Brouwer Fixed Point Theorem
• Ham Sandwich Theorem
• Hilbert Space
• Banach Tarski Paradox
• Axiom Of Choice
• Converse Of Intermediate Value Theorem
• Connected Space
• Closed Sets
• Compact Space
• Subsequences

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Free Geometry Problems and Questions writh Solutions

Free geometry tutorials on topics such as perpendicular bisector, central and inscribed angles, circumcircles, sine law and triangle properties to solve triangle problems. Also geometry problems with detailed solutions on triangles, polygons, parallelograms, trapezoids, pyramids and cones are included. Polar coordinates equations, conversion and graphing are also included. More challenging geometry problems are also included.

Geometry Problems

• Triangle Problems . Triangle problems with detailed solutions.
• Congruent Triangles Examples and Problems with Solutions .
• Similar Triangles Examples and Problems with Solutions . Definition and theorems on similar triangles including examples and problems with detailed solutions.
• Equilateral Triangles Problems with Solutions .
• Isosceles Triangles Problems with Solutions .
• Area and Perimeter of Right Triangles Problems With Solution .
• Cosine Law Problems . The cosine law is used to solve word problems.
• Sine Law Problems . The sine law is used to solve word problems.
• Triangle Inscribed in a Circle - Problem With Solution . Inscribed right triangle problem with detailed solution.
• Circle Tangent to Right Triangle - Problem With Solution . Solve a right triangle whose sides are all tangent to a circle. Both the problem and its detailed solution are presented.
• Overlapping Circles Problem . Find the overlapping area of two circles: problem with detailed solutions.
• Sectors and Circles Problems . Problems, with detailed solutions, related to sectors and circles.
• Two Squares and a Circle - Problem With Solution . A problem, with a detailed solution, on a circle inscribed in one square and circumscribed to another, is presented.
• Two Circles and a Square - Problem With Solution . A problem, with a detailed solution, on a square inscribed in one circle and circumscribed to another is presented.

Quadrilaterals

• Rectangle Problems . Rectangle problems on area, dimensions, perimeter and diagonal with detailed solutions.
• Geometry Problems on Squares . Square problems on area, diagonal and perimeter, with detailed solutions.
• Parallelogram Problems . Word problems related to parallelograms are presented along with detailed solutions.
• Trapezoid Problems . Trapezoid problems are presented along with detailed solutions.
• Solve a Trapezoid Given its Bases and Legs .
• Rhombus Problems . Rhombus definition and properties are presented along with problems with detailed solutions.
• Polygons Problems . Problems related to regular polygons.
• Area Of Octagon - Problem With Solution . Find the length of one side, the perimeter and area of a regular octagon given the distance between two opposite sides (span).
• Angles in Parallel Lines and Transversals Problems . Problems related to parallel lines and alternate and corresponding angles.
• 3D Shapes Volume Problems . 3D shapes, such as prisms, volume problems with detailed solutions.
• Compare Volumes of 3D shapes . A problem to compare the volumes of a cone, a cylinder and a hemisphere.
• How to construct a frustum? . If you cut off the top part of a cone with a plane perpendicular to the height of the cone, you obtain a conical frustum. How to construct a frustum given the radius of the base, the radius of the top and the height?
• Cone Problems . Problems related to the surface area and volume of a cone with detailed solutions are presented.
• Pyramid Problems . Pyramid problems related to surface area and volume with detailed solutions.
• Intercept Theorem and Problems with Solutions .

Geometry Tutorials

• Parts of a Circle .
• Tangents to a Circle with Questions and Solutions .
• Intersecting Secant and Tangent Theorem Questions with Solutions .
• Inscribed and Central Angles in Circles . Definitions and theorems related to inscribed and central angles in circles are discussed using examples and problems.
• Intersecting Chords Theorem Questions with Solutions.
• Intersecting Secant Theorem Questions with Solutions.
• Semicircle Thales Theorem with questions and solutions
• Central and Inscribed Angles - Interactive applet . The properties of central and inscribed angles intercepting a common arc in a circle are explored using an interactive geometry applet.
• Triangles . Definitions and properties of triangles in geometry.
• Area of Triangles Problems with Solutions . Use different formulas of the area of a triangle to calculate the areas of triangles and shapes.
• Simple Proofs of Pythagorean Theorem and Problems with Solutions .
• Altitudes, Medians and Angle Bisectors of a Triangle .
• Triangles, Bisectors and Circumcircles - interactive applet . The properties of perpendicular bisectors in triangles and circumcircles are explored interactively using a geometry Java applet.
• Quadrilaterals , properties and formulas.
• Kite Questions with Solutions .
• Angles in Geometry . Definitions and properties of angles in geometry including questions with solutions.
• Angles in Parallel Lines and Transversals . This tutorial is about the corresponding, interior and exterior angles formed when a transversal line intersects two parallel lines.
• Latitude and Longitude Coordinate System .
• Find the GPS Latitude and Longitude Using Google Map .
• Regular Polygons . Tutorial to develop useful formulas for area of regular polygons.

Other Geometry Topics

• Perpendicular Bisector Problems with Solutions .
• Table of Formulas for Geometry . A table of formulas for geometry, related to area and perimeter of triangles, rectangles, circles, sectors, and volume of sphere, cone, cylinder are presented.

Challenge Geometry Problems

• Two Tangent Circles and a Square - Problem With Solution . You are given the perimeter of a small circle to find the radius of a larger circle inscribed within a square.
• Kite Within a Square - Problem With Solution . A problem on finding the sine of the angle of a kite within a square.
• Solve Triangle Given Its Perimeter, Altitute and Angle - Problem With Solution .
• Solve Right Triangle Given Perimeter and Altitude - Problem With Solution .
• Triangle and Tangent Circle - Problem With Solution . A problem, on a triangle tangent at two points to a circle, is presented along with detailed solution.
• Three Tangent Circles - Problem With Solution . A problem, on three tangent circles, is presented along with solution.
• Equilateral Triangle Within a Square - Problem With Solution . A problem on the proof of an equilateral triangle within a square is presented along with detailed solution.
• Square Inscribed in Right Triangle - Problem With Solution . Find the side of a square inscribed in a right triangle given the sides of the triangle.

Polar Coordinates

• Plot Points in Polar Coordinates . An interactive tutorial on how to plot points given by their polar coordinates.
• Graphing Polar Equations . This is tutorial on graphing polar equations by hand, or sketching, to help you gain deep understanding of these equations. Several examples with detailed solutions are presented.
• Convert Polar to Rectangular Coordinates and Vice Versa . Problems, with detailed solutions, where polar coordinates are converted into rectangular coordinates and vice versa are presented.
• Convert Equation from Rectangular to Polar Form . Problems were equations in rectangular form are converted to polar form, using the relationship between polar and rectangular coordinates, are presented along with detailed solutions.
• Convert Equation from Polar to Rectangular Form . Equations in polar form are converted into rectangular form, using the relationship between polar and rectangular coordinates. Problems with detailed solutions are presented.

Geometric Transformations

• Reflection Across a Line . The properties of reflection of shapes across a line are explored using a geometry applet.
• Rotation of Geometric Shapes . The rotations of 2-D shapes are explored.

Geometric Calculators and Worksheets

• Online Geometry Calculators and Solvers : Several calculators to help in the calculations and solutions of geometry problems.
• Free Geometry Worksheets to Download

Geometry Math Problems - Perimeters

In these lessons, we will learn to solve geometry math problems that involve perimeter.

Related Pages Geometry math problems involving area Area Formula Geometry math problems involving angles More Algebra Word Problems

Geometry word problems involves geometric figures and angles described in words. You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Geometry Word Problems Involving Perimeter

Example: A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?

Solution: Step 1: Assign variables:

Let x = length of the equal sides Sketch the figure

Step 2: Write out the formula for perimeter of triangle .

P = sum of the three sides

Step 3: Plug in the values from the question and from the sketch.

50 = x + x + x+ 5

Combine like terms 50 = 3x + 5

Isolate variable x 3x = 50 – 5 3x = 45 x = 15

Be careful! The question requires the length of the third side.

The length of third side = 15 + 5 = 20

Answer: The length of third side is 20.

Geometry Math Problem involving the perimeter of a rectangle

The following two videos give the perimeter of a rectangle, a relationship between the length and width of the rectangle, and use that information to find the exact value of the length and width.

Example: A rectangular garden is 2.5 times as long as it is wide. It has a perimeter of 168 ft. How long and wide is the garden?

Example: A rectangular landing strip for an airplane has perimeter 8000 ft. If the length is 10 ft longer than 35 times the width, what is the length and width?

Examples of perimeter geometry word problems This video shows how to write an equation and find the dimensions of a rectangle knowing the perimeter and some information about the about the length and width.

Example: The width of a rectangle is 3 ft less than its length. The perimeter of the rectangle is 110 ft. Find the dimensions.

Perimeter Word Problems

Example: The length of a rectangle is 7 cm more than 4 times its width. Its perimeter is 124 cm. Find its dimensions.

Geometry Math Problem involving the perimeter of a triangle

The following two videos give the perimeter of a triangle, a relationship between the sides of the triangle, and use that information to find the exact value or values of the required side or sides.

Example: Patrick’s bike ride follows a triangular path; two legs are equal, the third is 8 miles longer than the other legs. If Patrick rides 30 miles total, what is the length of the longest leg?

Example: The perimeter of a triangle is 56 cm. The first side is 6 cm shorter than the second side. The third side is 2 cm shorter than twice the length of the first side. What is the length of each side?

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• Analyzing categorical data
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• Prepare for the 2020 AP®︎ Statistics Exam
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• Polynomials
• Composite functions
• Probability and combinatorics
• Limits and continuity
• Derivatives: definition and basic rules
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• Applications of derivatives
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• Parametric equations, polar coordinates, and vector-valued functions
• Applications of integrals
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• AP Calculus AB solved free response questions from past exams
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• Integrating multivariable functions
• Green’s, Stokes’, and the divergence theorems
• First order differential equations
• Second order linear equations
• Laplace transform
• Vectors and spaces
• Matrix transformations
• Alternate coordinate systems (bases)

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Geometry: Common Core (15th Edition)

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