The square and the midline of a triangle

A segment joining the midpoints of two sides of a triangle is called its midline. Every triangle has three midlines. Theorem: the midline of a triangle is parallel to the third side and equals half of it. In the proof we extend the midline by its own length and obtain a parallelogram. Consequence: the triangle whose vertices are the midpoints of the sides has half the perimeter of the original triangle. If we join the midpoints of the sides of a convex quadrilateral in order, we get a parallelogram.