Question
Given that ∠A = ∠P and AC = PR. Then, which of the following conditions are true for Δ PQR and Δ ABC to be congruent.
- BC = QR by ASS criteria
- BC = QR by SSA criteria
- AB = PQ by SAS criteria
- AB = PQ by SSA criteria
Hint:
If two sides and the included angle of a triangle is equal to the two sides and the included angle of another triangle, then the two triangles are said to be congruent by SAS congruence criteria.
The correct answer is: AB = PQ by SAS criteria
If two sides and the included angle of a triangle is equal to the two sides and the included angle of another triangle, then the two triangles are said to be congruent by SAS congruence criteria. Only SAS congruence criteria holds true not ASS or SSA rule.
In Δ PQR and Δ ABC,
∠P = ∠A (given),
AC = PR (given),
Δ PQR and Δ ABC will be congruent by SAS rule only when AB = PQ.
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