Consider and in which the following measurements are given:

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

Problem

Consider △PQR\triangle PQR and △STU\triangle STU in which the following measurements are given: PQ=5 cm,  PR=7 cm,  ∠QPR=62∘PQ = 5\,\text{cm},\; PR = 7\,\text{cm},\; \angle QPR = 62^{\circ} ST=5 cm,  SU=7 cm,  ∠TSU=62∘ST = 5\,\text{cm},\; SU = 7\,\text{cm},\; \angle TSU = 62^{\circ} (i) Determine whether the two triangles are congruent. Give full reasons for your answer. (ii) Write the correct correspondence of their vertices (for example, △PQR≅△…\triangle PQR \cong \triangle \ldots). (iii) If QR=4.6 cmQR = 4.6\,\text{cm}, find the length of TUTU.

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