Question

In AABC and APQR, ZABC = ZPQR,
seg BD and seg QS are angle bisectors.
If!(AD) _!(DC)
(PS) (SR)
Prove that AABC - APQR.​

Answer 1

Answer:

According to the problem,

In triangle ABC, BD is the angle bisector

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

Similarly, in triangle QPR, 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 QPR.