Master

Congruent Figures

Master congruent figures with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Congruent Figures

Study Guide

Key Definition

Congruent figures are geometric figures that have the same shape and size. If you can transform one figure into another by a sequence of translations, rotations, and/or reflections, then the two figures are congruent.

Important Notes

When naming congruent polygons, the order of vertices must correspond so that each side and angle matches its counterpart; for example, if hexagon ABCDEF is congruent to hexagon OJKLMNOP, you must list vertices in matching order.
For polygons, if all the corresponding angles and corresponding sides are congruent, then the polygons are congruent.

Mathematical Notation

$\cong$ is used to denote congruence between two figures.

Remember to use the congruence symbol when stating that two figures are congruent.

Why It Works

Congruence is a fundamental concept in geometry, and it works because it's based on the notion that a shape remains the same if it's moved or rotated. This is a fundamental property of space itself.

Remember

Congruence is about shape and size. If two figures are congruent, you can turn, flip, and/or slide one so it fits exactly on the other.

Quick Reference

Congruence:$\cong$

Understanding Congruent Figures

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Congruent figures are the same in shape and size. If you can move one to match perfectly with the other, they are congruent.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following conditions is sufficient to prove two triangles congruent?

Real-World Problem

Question Exercise

Intermediate

Building a Fence

You're helping your dad build a square fence around your backyard. He tells you that the fence needs to have congruent sides for aesthetics and balance. If one side is 10 feet long, how long should the other sides be?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Can a circle be congruent to a square? Why or why not?

Challenge Quiz

Single Choice Quiz

Advanced

Two regular hexagons have side lengths of 5 cm and 10 cm, respectively. Are they congruent?

Recap

Watch & Learn

Review key concepts and takeaways