Question

Prove that 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. 

In the given figure, DE|| AC and DF|| AE.

Prove that: BF/FE=BE/EC

Answer 1

Given: A triangle ABC in fig. (i) in which a line parallel to side BC intersects other two sides AB and AC at D and E respectively.

To Prove: AD/DB=AE/EC

Construction: Join BE and CD and then draw DM ⊥ AC and EN ⊥ AB.

Now, ΔBDE and ΔDEC are on the same base DE and between the same parallel lines BC and DE.
So,  ar(ΔBDE) =       ar(ΔDEC)                                 ..(iii)