In the given figure, $DE \| OQ$ and $DF \| OR$. Show that $EF \| QR$.
"

Given:

$DE \| OQ$ and $DF \| OR$.

To do:

We have to show that $EF \| QR$.

Solution:

We know that,

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

In $\triangle POQ, DE \| OQ$,

This implies,

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

In $\triangle POR, DF \| OR$,

This implies,

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

From (i) and (ii), we get,

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

By converse of B.P.T.,

$EF \| QR$

Hence proved.

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Updated on: 10-Oct-2022

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