ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced at Q. Prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC.

Question

Philoid · Accepted Answer

Given :- ABCD is a parallelogram

To prove :- BP x DQ = AB x BC

Proof:- In ΔABP and ΔQDA

Then, ΔABP ~ ΔQDA

SO, (Corresponding parts of similar triangle area proportion) But, DA = BC (Opposite side of parallelogran)

Then,

Or, AB x BC = QD X BP