# Maths Q:D is the midpoint of the side BC of triangle ABC, If P and Q are points on AB and AC such that DP bisects angle BDA and DQ bisects angle ADC , then prove that PQ is parallel to BC.

1
by LAHI

2015-08-26T02:40:00+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
The angular bisector of angle in a triangle divides the opposite segment, in the same ratio as the other two sides.

=>  AB/AP = 1 + BD/AD
=> (CQ + AQ)/AQ = 1 + CD/AD
=>  AC/AQ = 1 + CD/AD

since CD = BD,  D is the midpoint of BC,

AB/AP  =  AC / AQ        or  AB/ AC = AP / AQ

AB is parallel to AP  and AC is parallel to AQ.  And corresponding ratios are same.  The angle A is common in the two triangles ABC and APQ.

Hence, the two triangles  ABC and  APQ are similar.

Hence, PQ is parallel to BC.

click on thanks button above