Question

In triangle ABC and triangle PQR,angle ABC is congruent angle PQR,seg BD and seg QS are angle bisectors.If length(AD)/Length (PS) =length (DC)/length SR
Prove that :∆ABC~∆PQR

Answer 1

Answer:

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/DS=PQ/QR

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 ΔABC∼ΔPQR.