Question

7.
In the adjacent figure, A, B and C are points OP,QR
and OR respectively such that AB || PQ and AC||PR.
Show that BC || QR.​

Answer 1

Answer:

In △OPQ, we have

AB∥PQ

Therefore, by using basic proportionality theorem , we have

AP

OA

=

BQ

OB

.................(i)

IN △OPR, we have

AC∥PR

Therefore, by using basic proportionality theorem , we have

CR

OC

=

AP

OA

.................(ii)

Comparing (i)&(ii), we get

BQ

OB

=

CR

OC

Therefore, by using converse of basic proportionality theorem, we get

BC∥QR

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Answer 2

Answer:

I n triangle PQR,....(1)

now in trangle POQ

AB//PQby thales therom

so,OA/AP=OB/BQ.........(2)

now in tranglePOR

OA/AP=OC/CR.......(3)

from eq 1,2and 3

OC/CR=OB/BQ

= by thales theorem

BC//QR