Question

if p,q are the mid points of two line segments AB and CD respectively and AP=QD then show that AB=CD

Answer 1

if p is the midpoint of AB
and q is the midpoint of CD
now, Ap = Bp ---------------(1)
& Cq = Dq -------------------(2)
if Ap = QD
or, 2 Ap = 2QD
or, AP+ BP = CQ+ QD [ from (1)&(2) no.]
or, AB = CD ( proved)
I hope you will understand...

Answer 2

We know by the question that P and Q are the mid point of line segment AB and CD therefore AP=PB ,CQ=QD

If AP is also equal to QD then sure PB=CQ

THEREFORE
AB=CD