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ASA (Angle-Side-Angle) Postulate

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ASA (Angle-Side-Angle) Postulate

Study Guide

Key Definition

The ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles must be congruent.

Important Notes

The included side is the side that is between the two angles.
ASA is a method to test the congruence of triangles.
Congruence in triangular geometry means that two triangles have the same shape and size, but one may be a mirror image of the other.

Mathematical Notation

$\cong$ symbol is used to indicate congruence in geometry.

$\angle$ is the symbol for angle.

$\triangle$ is the symbol for triangle.

Remember to use proper notation when solving problems

Why It Works

ASA postulate works because if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, it is enough to say that the two triangles are congruent.

Remember

The ASA postulate can only be used when two angles and the included side are known to be equal.

Quick Reference

ASA Postulate:$\angle B \cong \angle E, BC \cong EF, \angle C \cong \angle F \Rightarrow \triangle ABC \cong \triangle DEF$

Understanding ASA (Angle-Side-Angle) Postulate

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Video explanation of this concept

Beginner

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Beginner Explanation

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Given that $\angle B \cong \angle E, BC \cong EF, \angle C \cong \angle F$, what can we conclude?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

John and Mary have each drawn a triangle. John's triangle has two angles and the included side between those angles equal to two angles and the included side of Mary's triangle. Are their triangles congruent?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Can we determine triangle congruence if we know only the three angles of the triangles?

Challenge Quiz

Single Choice Quiz

Advanced

If we know that $\angle X \cong \angle M, \angle Y \cong \angle N$, and $XY \cong MN$, which postulate can we use to prove that $\triangle XYZ \cong \triangle MNO$?

Recap

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