Question

In the following figure, DE || OQ and DF || OR, show that EF || QR

Answer 1

To Prove: EF||QR
Proof:

In ∆ POQ, DE || OQ
∴ $\frac{PE}{EQ}=\frac{PD}{DO}$ (basic proportionality theorem)....(i)

In ∆POR, DF||OR
∴ $\frac{PF}{FR}=\frac{PD}{DO}$ (basic proportionality theorem)....(ii)

From (i) and (ii), we obtain,
$\frac{PE}{EQ}=\frac{PF}{FR}$
∴ EF||QR

Hence Proved.