A is given. If lines are drawn through parallel respectively to the sides and forming as shown in the adjoining figure, show that

Question

Philoid · Accepted Answer

Here given that BC || QA and CA || QB which means that BCQA is a parallelogram.

∴ BC = QA …(1)

Similarly, BC || AR and AB || CR, which means BCRA is a parallelogram.

∴ BC = AR …(2)

But QR = QA + AR
From (1) and (2), we get,
QR = BC + BC

∴ QR = 2BC

Hence, BC = QR