Question

In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Answer 1

To Prove: BC || QR
Proof:

In ∆ POQ, AB || PQ
∴$\frac{OA}{AP}=\frac{OB}{BQ}$............(i)

In ∆ POR, AC||PR
∴$\frac{OA}{AP}=\frac{OC}{CR}$...........(ii)

From (i) and (ii) we obtain,
$\frac{OB}{BQ}=\frac{OC}{CR}$

∴ BC || QR

(By the converse of the basic proportionality theorem)

Hence Proved