Question

In the given 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

Given: In △PQR, AB || PQ; AC || PR 

R.T.P : BC || QR 

Proof: In △POQ; AB || PQ 

\(\frac{OA}{AP}=\frac{OB}{BQ }\)= ……… (1) 

∵ Basic Proportional theorem) 

and in △OPR, 

Proof: In △POQ; AB || PQ

\(\frac{OA}{AP} \) = \(\frac{OC}{CR }\)……… (2) 

From (1) and (2), we can write

\(\frac{OB}{BQ}=\frac{OC}{CR }\)---(3)

Then consider above condition in △OQR then from (3) it is clear. 

∴ BC || QR [∵ from converse of Basic Proportionality Theorem] 

Hence proved.