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.