Question

In the figure, ABCD is parallelogram and AP = CQ

Prove that PBQD is a parallelogram

Answer 1

DC = AB ………. (1)

AD = CB

QC = AP ……. (2) (as ABCD is a parallelogram)

(1) – (2) ⇒ DC – QC = AB – AP; 

∴ DQ = PB When, ∆ APD, ∆ CQB are considered.

AD = CB

AP = QC

∠A = ∠C, The two sides and angle formed by them in these triangles are equal. So the third sides PD and BQ are equal.

∴ Two pairs of opposite sides in the quadrilateral PBQD are equal. So PBQD is a parallelogram.