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

    exAngle Side Angle Congruencyple of Angle Side Angle Congruency
    If ∠P≅∠T, and , and ∠S≅∠R, then ΔPQS≅ΔQRT.

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


Solved Example Clockple on Angle Side Angle Congruency

Ques: Which of the figures satisfies the ASA congruence condition?

    Angle Side Angle Congruencyple of Angle Side Angle Congruency

Choices:

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

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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