How to Prove Diagonals Bisect in a Parallelogram

[tinfoilhat]

I'm not sure how to go about this problem; I'd love a kick in the right direction.

Prove that the diagonals of a parallelogram bisect each other.

 

[Sonty]

Think of it in this terms: what if they don't? what happens then?

 

[HallsofIvy]

Since this is titled "linear algebra question", do this:

Set up a coordinate system so one corner of the parallelogram is at (0,0) and one side along the x-axis. Then another vertex is at (a, 0), a third at (b,c) and the fourth at (a+b,c).

Now find the midpoint of each diagonal.