Proof of the Midsegment Theorem for Triangles

A quick algebraic proof of a geometric concept. We show that the line connecting the middle points of two sides of a triangle is half the length of the third side. While some proofs do this from Thales Theorem, or by geometric considerations, we use the fact that the ‘middle’ between two points is the average of the two points: that is, the coordinate-wise sum of their positions divided by two. The proof has a nice graphical structure, making a pretty and insightful equation-picture (point 3 in the interactive).

If you're not sure what to do, here's a video of me walking through this example: