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

Angle Angle Side Congruencyple 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.


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.

exAngle Angle Side Congruencyple of Angle Angle Side Congruency

Choices:

  • A. 220
  • B. 700
  • C. 1100
  • D. 480

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 = 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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