Question

In given figure, If DE||AQ and DF||AR. Prove that EF||QR.

Answer 1

In $△PQA$, we have

$DE||AQ$ [Given]

Therefore, by basic proportionality theorem, we have

$\frac{PE}{EQ}=\frac{PD}{DA}$........(i)

In $△PAR$, we have

$DF||AD$ [Given]

Therefore, by basic proportionality theorem, we have

$\frac{PD}{DA}=\frac{PF}{FR}$........(ii)

From (i) and (ii), we have

$\frac{PE}{EQ}=\frac{PF}{FR}$

$\Rightarrow$ $EF||QR$ [By the converse of Basic Proportionality Theorem]