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 triangle BPQ is isosceles.
Given that P is a point on the bisector of an angle ABC, and PQ|| AB.
We have to prove that ΔBPQis isosceles
BP is bisector of ∠ABC⇒∠ABP=∠PBC ............(1)
⇒ ∠BPQ=∠ABP ................(2)
From (1) and (2), we get
In , ΔBPQ
⇒ΔBPQ is an isosceles triangle.
Concept: Properties of a Triangle
Is there an error in this question or solution?
Video TutorialsVIEW ALL 
Video Tutorials For All Subjects
- Properties of a Triangle