Given : DE || OQ
DF || OR
Show that : EF || QR
Proof :
In ΔPQO,
DE || OQ
[by converse of basic
proportionality theorem]
P
Q
R
E
F
D
O
...(i)
... [by basic proportionality theorem.]
In ΔPRO,
DF || OR
... [by basic proportionality theorem.]
=
PF
FR
=
PD
DO
... from (i) and (ii)
In ΔPQR,
PE
EQ
PF
FR
=
...(iii)
... from (iii)
PE
EQ
=
PD
DO
∴
PE
EQ
PF
FR
EF || QR
...(ii)
Ex 6.2 - 5
∴