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