[" 4.Pisa point on the bisectorof "/_ABC" .If the line through "P" ,parallel to BA meet BC "],[" at "Q" ,prove that "BPQ" is an isosceles trianale "]

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

P is a point on the bisector of angle ABC .If the line through P,parallel to BA meet at Q ,prove that BPO is an isosceles triangle.

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.

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

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.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Prove that BDFE is a parallelogram

In triangle ABC, P is the mid-point of side BC. A line through P and parallel to CA meets AB at point Q and a line through Q and a line through Q and parallel to BC meets median AP at point R. Prove that : BC=4QR .

P is the mid point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. prove that AR=2BC.

P is the mid point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. prove that BR=2BQ.

In triangle ABC, P is the mid-point of side BC. A line through P and parallel to CA meets AB at point Q and a line through Q and parallel to BC meets median AP at point R. Prove that : AP=2AR