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# One angle of a triangle is equal to one angle of another triangle and the bisectors of these equal angles divide the opposite sides in the same ratio. Prove that the triangles are similar.( I want to know how this id directly assumed during the proof: the ratio of the corresponding sides=the ratio of the bisected side)

Asked by sajal2402 12th February 2019, 10:36 AM
Angle bisector theorem :- anglar bisector of an angle of triangle divides the opposite side in same ratio as their sides of the smae angle.

In ΔABC, AD is bisector of B , hence
In the figure, In triangles ABC and PQR, B = P .  AD and PS are respective angular bisector.
then we have   ...........................(1)
.............................(2)
Given : bisectors of B and P divides the opposite side in same ratio,  hence .........................(3)
By comparing (1), (2) and (3), we have ..........................(4)
In ΔABC and ΔPQR, B = P and the sides of these equal angles are in same ratio.  Hence ΔABC and ΔPQR are similar triangles
Answered by Expert 12th February 2019, 11:17 AM
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