Because AP4=CP4, P5P4=P3P4.

According to one of the judging theorems of parallelogram, quadrilaterals whose diagonals bisect each other are parallelograms.

The quadrilateral AP5CP3 is a parallelogram.

Similarly, it can be proved that quadrilateral AP6CP2 and quadrilateral AP7CP 1 are also parallelograms.

hope this helps