The Varignon Quadrilateral from Vectors.

I created Points A, B, C, D and made vectors linking the points in that order. The vectors are a, b, c, d.

The points and vectors were set up in the default to be irregular. Points A, B, C, D can be manipulated to make another quadrilateral of your choice.

I then created four vectors that are half the lengths of a, b, c, d. They are:
u = 0.5(a+b)
v = 0.5(b+c)
w = 0.5(c+d)
z = 0.5(d+a)
I then applied these to points A, B, C, D to create vectors e, f, g, h which are in light blue.

Their endpoints are A', B', C', D'. They are the midpoints of Quadrilateral ABCD. I created a quadrilateral from them, and measured the interior angles.

Watch the interior angles, and see if you notice what type of Quadrilateral A', B', C', D' is no matter how you move A, B, C, or D.

Darron Steele, Created with GeoGebra