Question

X and y are midpoints of side ac and ab of triangle abc respectively. A straigt horizontal line is drawn through vertex a of triangle such that qp||bc, and cyq and bxp are straight lines. Prove that area▲(abp)=area▲(acq). Please urgent. .needed

Answer 1

I have attached the figure along with it the figure is a little bit clumsy!!!!!!
In ▲ABC , X and Y are the midpoints of sides AC and AB
XY||CB and XY||PQ  (Mid Point Theorem)
▲XYB and ▲XYC are on the same base XY and between same parallels XY and CB
Therefore,ar(XYB)=ar(XYC)....................equation 1
If it is given that A is the mid point of PQ then only we can prove the rest
then XY=PA AND XY=AQ
in quadrilateral PAYX and AQYX
since one pair of opposit sides are equal and parallel these two are parallelograms
Parallelograms PAYX AND AQYX are on the same base XY and between same parallels XY and PQ
therefore ar(PAYX)=ar(AQYX).............equation 2
equation 1 +equation 2
ar(ABP)=ar(ACQ)
Hence Proved