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Muhammadowais:
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Step-by-step explanation:
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/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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