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

Given, DE ||OQ and DF || OR

Need to prove that EF || QR

⇒ Let us consider Δ POQ

⇒ By Basic proportionality theorem we have if a line drawn to one side of a triangle intersects the other two sides in distinct points, then it divides the other 2 side in the same ratio.

∴ ………………………eq(1)

⇒ Consider Δ POR

⇒ DF || OR

∴ …………………eq(2)

⇒ From eq(1) and eq(2) we have

⇒

∴ By converse of basic proportionality theorem we have if a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.

∴ EF || QR

Hence proved