[by converse of basic proportionality theorem]
A, B & C are points on OP, OQ and OR respectively
such that AB || PQ, AC || PR
Show that : BC || QR
Proof :
In ΔPOQ,
AB || PQ
... [given]
Q
R
P
A
B
C
O
BC || QR
...(i)
OB
BQ
=
OA
AP
... [by basic proportionality theorem.]
In ΔPOR,
AC || PR
... [given]
...(ii)
... [by basic proportionality theorem.]
=
OC
CR
=
OA
AP
... from (i) and (ii)
In ΔOQR,
OB
BQ
OC
CR
=
...(iii)
... from (iii)
OB
BQ
OC
CR
∴
Ex 6.2 - 6