Question

Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

 Using the above result, do the following.

In figure, DE ||AC and DC ||AP.

Prove that BE/BC =BC/CP.

Answer 1

Given: A triangle ABC 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)