Question

in triangle ABC and triangle PQR angle ABC congruent to angle ABC seg BD and seg qs angle bisector if length of AD upon length of PS equal to length of DC upon length of RS prove that triangle ABC congruent to Triangle 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.

Step-by-step explanation:

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