Connecting Midpoints

In the diagram below, we have connected the midpoints of AC and BC.

The well-known theorem here in elementary Euclidean geometry is that MN is parallel to, and half the length of, AB.

How can we prove this?

As always, try to come up with a couple of different approaches.  What are some consequences of theorem?  What are some natural extensions to this situation?

 

www.MrHonner.com

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