If you draw any triangle, locate the midpoints of two sides, and draw a segment between these midpoints, it appears that this segment is parallel to the third side and half its length:

This result follows from a very important theorem, called the Triangle Midsegment Theorem, which also leads to results about similarity of figures. (Two figures are said to be similar if they have the same shape, but not necessarily the same size.)

Triangle Midsegment Theorem:      

A segment joining two sides of a triangle, parallel to the third side, and containing the midpoint of one of the two sides also contains the midpoint of the other side, and is half the length of the parallel side.

Given:	M is the midpoint of , N is on , and
Prove:	N is the midpoint of  and