We began by discussing the Triangle Midpoints Theorem. We then went on to construct a triangle in the XY-plane, used the Midpoint Theorem to find the midpoints of two of the sides and connected the midpoints with a segment. We used coordinates to find the slopes of the two segments and compared them (equal, ergo parallel!) and used the distance formula to find the lengths of the parallel segments. The shorter length was exactly one-half the longer length. QED!