In the parallelogram avsd, the diagonals intersect at the point about m the middle of the BO.

In the parallelogram avsd, the diagonals intersect at the point about m the middle of the ВO. P is the middle of KO prove that AMCP is a parallelogram.

Since AВСD is a parallelogram, then its diagonals ВD and AC, at the point of intersection O are divided in half. AO = CO, BO = DO.

Point M is the middle of ВO, then ВM = MO, point P is the middle of DO, then DР = PO.

Since ВO = DO, then MO = RO.

Then in the quadrangle ABCP MP and AC are diagonals, and point O divides them in half, therefore, AMCP is a parallelogram, according to the third criterion, which was required to be proved.