- AM=BM [midpoint].
- < AMP = <MBQ [Corresponding angles for parallel lines cut by an transversal].
- <BQM=<QCP=<APM [Corresponding angles for parallel lines cut by an transversal].
- <BMQ=<MAP [When 2 pairs of corresponding angles are congruent in a triangle, the third pair is also congruent.]
- AMP is congruent to MBQ. [ASA]

Since midpoints are unique, and the lines connecting points are unique, the proposition is proven.

**Corollary:**
In any triangle, the lines connecting the midpoints are parallel to the
opposite sides and the four triangles created by these lines and the segments
of the original triangle formed by the midpoints are all congruent..