How to Prove Diagonals Bisect in a Parallelogram

AI Thread Summary
To prove that the diagonals of a parallelogram bisect each other, set up a coordinate system with one vertex at (0,0) and one side along the x-axis. Assign coordinates to the vertices: (0,0), (a,0), (b,c), and (a+b,c). Calculate the midpoints of both diagonals formed by these vertices. The midpoints will be equal, demonstrating that the diagonals bisect each other. This geometric property is essential in understanding the characteristics of parallelograms.
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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.
 
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Think of it in this terms: what if they don't? what happens then?
 
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.
 

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