Question

in triangle ABC and triangle PQR ‌ angle ABC congruent angle PQR seg QS are Angle bisector if AD /PS equal DC/SR prove triangle ABC congruent Triangle PQR

Answer 1

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Answer 2

Solution :-

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 ---------(I)

Similarly, in triangle PQR, QS is the angle bisector

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

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.

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@GauravSaxena01