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

# Angle Angle Side Congruency

## Definition of Angle Angle Side Congruency

Angle-Angle-Side (AAS) theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the two triangles are congruent.

### Examples of Angle Angle Side Congruency

∠L = ∠P = 450, ∠M = ∠Q = 1100, MN = QR = 12 m
The two angles and non-included side of △LMN are equal to the corresponding angles and non-included side of △PQR. So, both the triangles are congruent.

### Solved Example Clockple on Angle Angle Side Congruency

• A. 220
• B. 700
• C. 1100
• D. 480

#### Solution:

• Step 1: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the two triangles are congruent. [AAS theorem]
• Step 2: △ABC ≅ △DEF [Given]
• Step 3: ∠B = ∠E = 1100 and AB = DE = 12 cm
• Step 4: Since ∠C = 480, ∠F = 480 [△ABC and △DEF are congruent by AAS property.]
• Step 5: ∠D + ∠E + ∠F = 1800 [Sum of the angles in a triangle is 1800.]
• Step 6: ∠D + 1100 + 480 = 1800 [Substitute the values.]
• Step 7: ∠D = 220

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