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In the given triangles, ∠A = ∠P and AC = PR. Which of the following conditions are true for ΔPQR and ΔABC to be congruent?

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AB = PQ by SSA rule

PQ = AB by SAS rule

BC = QR by ASS rule

QR = BC by SSA rule

answer is A.

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Detailed Solution

If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent by the SAS congruence rule.

We know only the SAS congruence rule holds but not ASS or SSA rule.

In ΔPQR and ΔABC,
∠P = ∠A (Given)
PR = AC (Given)

Thus, ΔPQR and ΔABC will be congruent by the SAS rule only when PQ = AB.

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