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Properties of Congruence

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Properties of Congruence

Study Guide

Key Definition

Congruence means two figures have the same shape and size. If $\angle A \cong \angle B$, then they are congruent angles.

Important Notes

Congruent figures have equal corresponding angles and sides.
The Reflexive Property: $\angle A \cong \angle A$
The Symmetric Property: If $\angle A \cong \angle B$, then $\angle B \cong \angle A$
The Transitive Property: If $\angle A \cong \angle B$ and $\angle B \cong \angle C$, then $\angle A \cong \angle C$
Congruence applies to angles, line segments, triangles, and more.

Mathematical Notation

$\cong$ means congruence

Remember to use proper notation when solving problems

Why It Works

Congruence properties are fundamental because they help identify and prove geometric congruence using $\angle$ and $\triangle$ relations.

Remember

The properties of congruence are similar to equality properties, such as $a = a$.

Quick Reference

Reflexive Property:$\angle A \cong \angle A$

Symmetric Property:$\angle A \cong \angle B \Rightarrow \angle B \cong \angle A$

Transitive Property:$\angle A \cong \angle B \land \angle B \cong \angle C \Rightarrow \angle A \cong \angle C$

Understanding Properties of Congruence

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The reflexive property states that any figure is congruent to itself. For example, $\angle A \cong \angle A$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the reflexive property of congruence for an angle $\angle A$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You are designing a triangular garden. If two angles of the garden are congruent to each other and a third angle is congruent to one of these, what can you conclude about the angles?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $\angle A \cong \angle B$, what can be said about $\angle B$ and $\angle A$?

Challenge Quiz

Single Choice Quiz

Advanced

If $\triangle ABC \cong \triangle DEF$ with corresponding vertices A↔D, B↔E, C↔F, which of the following is true?

Recap

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