In parallelogram a diagonal is drawn

MATHEMATICS · Subjective · CBSE · Mathematics · Quadrilaterals · Quadrilaterals

Problem

In parallelogram PQRSPQRS a diagonal PRPR is drawn. (i) List the pairs of opposite sides and the pairs of opposite angles of the parallelogram. (ii) Using only the basic definition of a parallelogram and its properties of opposite sides and opposite angles, explain why ∠QPR\angle QPR and ∠SRP\angle SRP are equal. (iii) Based on your answer to part (ii), give a reasoning (without writing a formal congruence proof) to show that triangles △PQR\triangle PQR and △RSP\triangle RSP have the same area.

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