Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a D ABC a shown in Fig.8.5. Show that BC = QR.

Question

Philoid · Accepted Answer

Given,

PQ||AB, PR||AC and RQ||BC.

In quadrilateral BCAR,

BR||CA and BC||RA

BCAR is a parallelogram

BC = AR …(i)

Now, in quadrilateral BCQA,

BC||AQ and AB||QC

BCQA is a parallelogram

BC = AQ …(ii)

Adding Eqn. (i) and (ii), we get

2BC = AR + AQ

2BC = RQ

Hence, proved.