﻿ Definition and examples of Angle Side Angle Congruency | Define Angle Side Angle Congruency - Geometry - Free Math Dictionary Online

# Angle Side Angle Congruency

## Definition of Angle Side Angle Congruency

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

### Examples of Angle Side Angle Congruency

If ∠P≅∠T, and , and ∠S≅∠R, then ΔPQS≅ΔQRT.

### Solved Example Clockple on Angle Side Angle Congruency

#### Choices:

A. Figure 2
B. Figure 1 and Figure 2
C. Figure 1
D. none of the above

#### Solution:

Step 1: ASA congruence condition: If the measures of two angles and one side in a triangle are equal to the measures of corresponding two angles and one side of another triangle, then the two triangles are congruent.
Step 2: From Figure 1, AC = CD and∠A ≅∠D, ∠ACB≅∠DCE.
Step 3: ΔABC≅ΔDCE by ASA congruency condition
Step 4: From Figure 2, QR = RT, PR = RS and ∠PRQ ≅ ∠SRT
Step 5: ΔPQR ≅ ΔSRT by SAS congruency condition
Step 6: Only Figure 1 satisfies the ASA congruence condition.

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