If ∆ABC and ∆QPR are congruent triangles such that AB = 7 cm, AC = 8 cm, ∠B = 65°, and ∠C = 75°, then which of the following is true?

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Accepted Answer

Given that ∆ABC and ∆QPR are congruent, corresponding sides and angles are equal.

1. Since AC corresponds to PR, AC = PR = 8 cm. Also, angle B corresponds to angle P, so ∠P = 65°.

2. Since AB corresponds to PQ, AB = PQ = 7 cm. Also, angle C corresponds to angle R, so ∠R = 75°.

3. The sum of angles in ∆ABC is 180°. Given ∠B = 65° and ∠C = 75°, ∠A = 180° - (65° + 75°) = 40°. Since ∠A corresponds to ∠Q, ∠Q = 40°. However, RQ is not a side of ∆QPR; the sides are PQ, PR, and QR. The side corresponding to AB (7 cm) is PQ, not RQ. Therefore, the statement '∠Q = 40° and RQ = 7 cm' is incorrect.

Hence, options 1 and 2 are correct.

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