Question

AP=AQ and BP=AQ.prove that AB is the bisectors of angle PAQ and PBQ?
In maths

Answer 1

Explanation:

Given: In angle ABC//lineBC and line/ intersects AB and AC ib point p and q respectively

To prove:- AP/PB = AQ/QC

construction:-Draw seg pc and seg bq

proof:- Angle APQ and angle AQB have equal height.

A(APQ)/ A(PQB) = AP/PB ...(1).(areas propertionate to bases.)

and A(APQ)/ A(PQC) = AQ/QC...(2).(areas proprotioatc to leaves.)

Seg PQ is common base of angle PQB and angle PQC seg PQ// seg BC, hence angle PQB and angle PQC have equal heights.

A(PQB)=A(PQC).......(3)

A(APQ)/A(PQB)= A(APQ)/ A(PQB),.....[from(1).(2)and(3)].

AP/PB = AQ/QC.....[from(1)and(2).]