In and the following measurements are given:

MATHEMATICS · Subjective · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

In △ABC\triangle ABC and △PQR\triangle PQR the following measurements are given: ∠A=55∘,  ∠C=47∘,  ∠P=55∘,  ∠R=47∘\angle A = 55^{\circ},\; \angle C = 47^{\circ},\; \angle P = 55^{\circ},\; \angle R = 47^{\circ}, AC=PR=6.5 cmAC = PR = 6.5\,\text{cm} and AB=8 cmAB = 8\,\text{cm}. (a) Prove that the two triangles are congruent. (b) Write the correct correspondence of their vertices. (c) Using the result of part (a), determine the length of side PQPQ.

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