O is any point on the diagonal PR of a parallelogram PQRS (Fig. 9.16). Prove that ar (PSO) = ar (PQO).

Question

TextDiagonal Divides Parallelogram into Congruent TrianglesNCERT Exemplar

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that (i) ∆ APB ≅ ∆ CQD (ii) AP = CQ

Prove that a diagonal of a parallelogram divides it into two congruent triangles.