Question

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

Proof:

Given here,

↪In ΔOPQ, AB || PQ

By using Basic Proportionality Theorem,

↪OA/AP = OB/BQ…………….(i)

Also given,

↪In ΔOPR, AC || PR

By using Basic Proportionality Theorem

↪∴ OA/AP = OC/CR……………(ii)

From equation (i) and (ii), we get,

↪OB/BQ = OC/CR

By converse of Basic Proportionality Theorem,

↪In ΔOQR, BC || QR.

Hence Proved!!

Answer 2

Given here,

In ΔOPQ, AB || PQ

By using Basic Proportionality Theorem,

OA/AP = OB/BQ…………….(i)

Also given,

In ΔOPR, AC || PR

By using Basic Proportionality Theorem

∴ OA/AP = OC/CR……………(ii)

From equation (i) and (ii), we get,

OB/BQ = OC/CR

Therefore, by converse of Basic Proportionality Theorem,

In ΔOQR, BC || QR.