Vector Geometry: Proving Quadrilateral PQRS is a Parallelogram

[serenaday]

Using vector methods:

The figure ABCD is a quadrilateral; P,Q,R,S are the midpoints of the sides AB, BC, CD and DA respectively. Prove that the quadrilateral PQRS is a parrallelogram.

 

[chiro]

Using vector methods:

The figure ABCD is a quadrilateral; P,Q,R,S are the midpoints of the sides AB, BC, CD and DA respectively. Prove that the quadrilateral PQRS is a parrallelogram.

I'm guessing you could use the pythagorean theorem to show that corresponding sides are equal thus parallel.