Question

Class 10 ch 6 triangle ex 6.2 question no 6

Answer 1

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Answer 2

Given : O is any point within ΔPQR, AB || PQ and AC || PR

To prove : BC || QR

Construction : Join BC

Proof : In ΔOPQ, we have

AB || PQ [Given]

Therefore By Basic Proportionality Theorem, we have

OAAP=OBBQ ......... (1)

In Δ OPR, we have

AC || PR [Given]

Therefore by Basic Proportionality Theorem, we have

OAAP=OCCR ............. (2)

From (1) and (2), we obtain that

OBBQ=OCCR

Thus, in ΔOQR, B and C are points dividing the sides OQ and OR in the same ratio. Therefore, by

the converse of Basic Proportionality Theorem, we have,

BC || QR