## Related Words

# 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 = 45^{0}, ∠M = ∠Q = 110^{0}, 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.

### Video Examples: AAS (Angle-Angle-Side) Congruence rule and Proof

### Solved Example Clockple on Angle Angle Side Congruency

**Ques: **Find ∠D, if △ABC and △DEF are congruent by AAS property.

#### Choices:

- A. 22
^{0} - B. 70
^{0} - C. 110
^{0} - D. 48
^{0}

Correct Answer: A

#### 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 = 110
^{0}and AB = DE = 12 cm - Step 4: Since ∠C = 48
^{0}, ∠F = 48^{0}[△ABC and △DEF are congruent by AAS property.] - Step 5: ∠D + ∠E + ∠F = 180
^{0}[Sum of the angles in a triangle is 180^{0}.] - Step 6: ∠D + 110
^{0}+ 48^{0}= 180^{0}[Substitute the values.] - Step 7: ∠D = 22
^{0}

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