Question

In triangle ABC and POR ,angle ABC =angle PQR , seg BD and QS are angle bisector. If l(AD)/l(PS)= l(DC)/l(SR) prove that triangle ABC ~ triangle PQR

Answer 1

The angle bisector of a triangle dividing one side into two segments; the ratio of the two segments is proportional to the ratio of the other two sides of the triangle.

According to the problem,

In triangle ABC, BD is the angle bisector

Then AD/DC=AB/AC ---------(1)

Similarly, in triangle PQR, QS is the angle bisector

Then PS/SR=PQ/QR ----------(2)

Given that AD/PS=DC/SR

Substitute AD=(DC.PS)/SR

On solving, AB/AC=PS/SR

Therefore AB/AC=PQ/SR

The sides are proportional to each other. Hence the triangle ABC~ triangle PQR.

Answer 2

Explanation:

the answer is in adjoining image

hope it helps you!