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