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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