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

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

PQRS is a parallelogram whose area is 180 cm² and A is any point on the diagonal QS. The area of ∆ ASR = 90 cm².