Question

In the given figure PQ II AB and PR II AC. Prove QR II BC

Answer 1

Hello

Given that : - PQ ॥ AB & PR ॥ AC.

To prove : - QR ॥ BC

Proof : -

Now,

In ∆AOB,

OP/PA = OQ/QB....(i) [By Basic proportionality theorem]

Similarly, In ∆AOC,

OA/PA = OR/RC .....(ii) [By Basic proportionality theorem.]

From (i) & (ii), we get,

OQ/BQ = OR/RC

Therefore, QR ॥ BC . [By converse of Basic proportionality theorem.]

Hence, proved.