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Step 1: Look at the figure and note down the given values

NOTE: DE || OQ, DF || OR.

Show  EF || QR

Step 2: According to the given data choose the suitable theorem to simplify

Apply the basic proportional theorem

THEOREM:  If a line is drawn parallel to one side of a triangle to intersect

the other two sides in distinct points, then the other two sides are divided

in the same ratio.

EXAMPLE:  In ∆POQ, DE || OQ

\frac{PE}{EQ}=\frac{PD}{DO}......................(1)

In ∆POR, DF || OR

\frac{PD}{DO} = \frac{PF}{FR} .................................(2)

Step 3: Compare the equations (1) and (2)

From equations we get \frac{PE}{EQ} = \frac{PF}{FR}

Step 4: Make sure that the sides of required triangle are divided in the same ratio or not.

NOTE: If sides are in the same ratio apply the converse of the

basic proportional theorem.

THEOREM: If a line divides any two sides of a triangle in the same ratio

then the line must parallel to the third side.

EXAMPLE:  In ∆PQR,

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

So, we can say that  EF || QR

Hence, proved  EF || QR