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Converse of Isosceles Triangle Theorem

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Converse of Isosceles Triangle Theorem

Study Guide

Key Definition

The Converse of Isosceles Triangle Theorem states that if two angles of a triangle are congruent then the sides opposite to these angles are also congruent.

Important Notes

In the Converse of Isosceles Triangle Theorem, the congruent sides are called legs and the third side is called the base.
The angles opposite the legs are called base angles and are congruent.

Mathematical Notation

$\angle$ denotes an angle.

$\cong$ denotes congruence.

Remember to use proper notation when solving problems

Why It Works

The property works because of the Angle-Angle-Side (AAS) congruence. If two angles and a non-included side of one triangle are equal to the corresponding two angles and side of another triangle, the triangles are congruent.

Remember

The Converse of the Isosceles Triangle Theorem can be proved using the Angle-Angle-Side (AAS) congruence.

Quick Reference

Converse of Isosceles Triangle Theorem:$\angle P \cong \angle Q \Rightarrow \overline{PR} \cong \overline{QR}$

Understanding Converse of Isosceles Triangle Theorem

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Video explanation of this concept

Beginner

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Beginner Explanation

The Converse of Isosceles Triangle Theorem states that if two angles of a triangle are congruent, then the sides opposite these angles are congruent.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

In triangle PQR, if $\angle P \cong \angle Q$, which of the following statements is true?

Real-World Problem

Question Exercise

Intermediate

Architect's Dilemma

An architect is designing a triangular park. She wants to have two angles of the park to be equal for aesthetic reasons. How will this decision affect the sides of the park?

Thinking Challenge

Thinking Exercise