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 Fig. 7 .45 DE || BC and BD = CE. Prove that ΔABC is an isosceles triangle.

Answer 1

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

Now, ΔBDE and ΔDEC are on the same base DE and between the same parallel lines BC and DE.