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

Example of Angle-Side-Angle (ASA) Congruency

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• If ∠P ≅ ∠T, and alt="" /> ≅ alt="" />, and ∠S ≅ ∠R, then ΔPQS ≅ ΔQRT.

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

Which of the figures satisfies the ASA congruence condition?

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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 ≅ ΔCDE by ASA
Step 4: From Figure 2, QR = RT, PR = RS and ∠PRQ ≅ ∠SRT
Step 5: ΔPQR ≅ ΔSRT by SAS
Step 6: Only Figure 1 satisfies the ASA congruence condition.

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

• Angle
• Congruent
• Corresponding Angle
• Side
• Triangle

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