Proof: from the question, MD is parallel and equal to NC and BN; AM is parallel and equal to BN, CN,

Quadrilateral AMCN and quadrilateral MDNB are parallelograms.

Connecting MN

Quadrilateral MDCN is a parallelogram.

∫ MD =1/2 ad CD =1/2 ad, so MD=CD.

So the parallelogram MDCN is rhombic.

∴ND⊥CM

Quadrilateral AMCN and quadrilateral MDNB are parallelograms.

∴AN//NC BM//DN

∴ Quadrilateral PMQN is a parallelogram

∠∠MPN = 90 degrees.

So the parallelogram PMQN is a rectangle.