Two triangles are described as follows: Triangle : , ,

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

Problem

Two triangles are described as follows: Triangle ABCABC: AB=5 cmAB = 5\,\text{cm}, AC=7 cmAC = 7\,\text{cm}, ∠BAC=50∘\angle BAC = 50^\circ. Triangle PQRPQR: PQ=7 cmPQ = 7\,\text{cm}, PR=5 cmPR = 5\,\text{cm}, ∠QPR=50∘\angle QPR = 50^\circ. Answer the following. (i) Are △ABC\triangle ABC and △PQR\triangle PQR congruent? Give a clear reason based on a standard congruence criterion. (ii) Write the correct correspondence of the vertices of the two triangles when they are superposed. (iii) If ∠ABC=60∘\angle ABC = 60^\circ, find the measure of ∠PRQ\angle PRQ with justification.

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