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.

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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