Q. 64.6( 5 Votes )

P is a point on the bisector of an angle ABC. If the line through P parallel to AB meets BC at Q, prove that the triangle BPQ is isosceles.

Answer :


Given that P is the point on the bisector of an angle ABC, and PQ AB


We have to prove that BPQ is isosceles


Since,


BP is the bisector of ABC = ABP = PBC (i)


Now,


PQ AB


BPQ = ABP (ii) [Alternate angles]


From (i) and (ii), we get


BPQ = PBC


Or,


BPQ = PBQ


Now, in


BPQ = PBQ


is an isosceles triangle



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