Question

PLEASE HELP!

Let ABCD be a quadrilateral. Show that the quadrilateral obtained by joining the midpoints of adjacent sides of ABCD is a parallelogram.

HINT: Let a, b, c and d be vectors representing the four sides of ABCD

ALSO: My professor said, you should be able to do this without resorting to coordinates.

Answer 1

I would ignore the tip, and use triangle similarity.

Since the lines divide both sides on 2 equal parts, the lines that form both a angles are equal so the sides would be paralel and the inner figure would be a parallelogram.

Answer 2

oh, sorry I used the same letters, my letters represent different things from yours, just clarifying.

Answer 3

Rather than a simple visual photo, this is more of a proof, involving vectors. This is for a linear algebra course. I started out with this visual first.