P is a point on the bisector of an ang...

`P` is a point on the bisector of an angle `/_A B Cdot` If the line through `P` parallel to `A B` meets `B C` at `Q` , prove that triangle `B P Q` is isosceles.

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We have,`/_1=/_2`
( BP is the bisector of`/_ABC`
`/_1=/_3 (PQ∥BA)`
`∠2=∠3=>PQ=BQ`
`/_\PBQ` is isosceles.

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