In a ∆PQR and ∆ ABC, ∠P = ∠A and AC = PR. Which of the following conditions is true for triangle PQR and ABC to be congruent?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. AB = PQ by SAS.
Given that
In ∆PQR and ∆ ABC, ∠P = ∠A and AC = PR.
If two sides and the angle between them of a triangle are equal to two sides and the angle between them of another triangle, then according to the SAS congruence criterion, the two triangles are said to be congruent.
Only SAS congruence criteria hold true, not the ASS or SSA rules.
In Δ PQR and Δ ABC,
∠P = ∠A ,
AC = PR ,
Δ PQR and Δ ABC will be congruent by the SAS rule only when AB = PQ.