Question

triangle abc is similar to triangle pqr.if the bisector of angle bac meets bc at point d and bisector of angle qpr meets qr at point m prove that ab/pq=ad/pm

Answer 1

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Answer 2

Proved that AB/PQ = AD/PM.

Given

To prove that AB/PQ = AD/PM

From the figure,

ΔABC ≅ ΔPQR

Where, AD bisects ∠BAC.    

            PM bisects ∠QPR.

From the two figures, comparing

           ∠A = ∠P           ;         ∠B = ∠Q        [ corresponding angles are equal ]

∠A = ∠P  ------> 1/2 ∠A = 1/2 ∠P

            ∠BAD = ∠QPM   ( where, AD and PM is the bisector of ∠A and ∠P )

In ΔBAD and ΔQPM,

             ∠B = ∠Q

             ∠BAD = ∠QPM

             ΔBAD ≅ ΔQPM  ( By AA ( Angle-Angle ) similarity )

Hence, AD/PM = BD/QM = AB/PQ  ( Corresponding sides are proportional )

Therefore, AB/PQ = AD/PM.

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