Two triangles and are drawn such that

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

Two triangles PQRPQR and STUSTU are drawn such that ∠PQR=∠STU\angle PQR = \angle STU, ∠PRQ=∠SUT\angle PRQ = \angle SUT and PQ=STPQ = ST. Answer the following questions. (a) Name the side that lies between the two equal angles in each triangle. (b) State with reason whether the given information is sufficient to conclude that △PQR≅△STU\triangle PQR \cong \triangle STU. Mention the congruence criterion you use. (c) If the triangles are congruent, list all pairs of corresponding equal sides and equal angles. (d) Explain whether the equality QR=TUQR = TU follows from the information provided. Give justification for your answer.

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