Question

Quadrilateral ABCP and Il gm ABCD are on the same base
AB. Diagonal AC bisects the quadrilateral. Prove that
PD || AC​

Answer 1

quadrilateral Abcp and Abcd are on same base

Ac bisects Abcp(given)

ar(∆Abc)=at(∆Apc). i

and ac also bisects parallelogram incidues into 2triangelsof equal area

ar(∆abc)=at(∆Acd)_2

from eq1and 2we get

They are lying an the same base AC and from the property if the area of two triangles lying on the same base equal area then they are lying between the two parallel lines

pd||Ac(hence prove)