Question

In ∆ ABC and ∆ PQR, ∠ ABC ≅ ∠ PQR, seg BD and seg QS are angle bisector. If l l (AD) (PS) = l l (DC) (SR) Prove that : ∆ ABC ∼ ∆ 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/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.