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 Angle-Angle-Side Congruency     Angle     Corresponding Angle     Congruent     Side     Triangle  

Angle-Angle-Side (AAS) Congruency
Definition of Angle-Angle-Side (AAS) 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.

Example of Angle-Angle-Side (AAS) Congruency

• ∠L = ∠P = 45°, ∠M = ∠Q = 110°, MN = QR = 12 m
The two angles and non-included side of ΔLMN are equal to the corresponding angles and non-included side of ΔPQR. So, both the triangles are congruent.

Solved Example on Angle-Angle-Side (AAS) Congruency

Find ∠D, if ΔABC and ΔDEF are congruent by AAS property.

Choices:
A. 22°
B. 70°
C. 110°
D. 48°
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: ΔABC ≅ ΔDEF [Given]
Step 3: ∠B = ∠E = 110° and AB = DE = 12 cm
Step 4: Since ∠C = 48°, ∠F = 48° [ΔABC and ΔDEF are congruent by AAS property.]
Step 5: ∠D + ∠E + ∠F = 180° [Sum of the angles in a triangle is 180°.]
Step 6: ∠D + 110° + 48° = 180° [Substitute the values.]
Step 7: ∠D = 22°

Related Terms for Angle-Angle-Side (AAS) Congruency

• Angle
• Corresponding Angle
• Congruent
• Side
• Triangle

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