Midpoint theorem (triangle)

The midpoint theorem or midline theorem states that if you connect the midpoints of two sides of a triangle then the resulting line segment will be parallel to the third side and have half of its length. The midpoint theorem generalizes to the intercept theorem, where you rather than using midpoints partition both sides in the same ratio.

${\displaystyle {\begin{aligned}&{\text{D and E midpoints of AC and BC}}\\\Rightarrow \,&DE\parallel AB{\text{ and }}2|DE|=|AB|\end{aligned}}}$

The converse of the theorem is true as well. That is if you draw a line through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.

The triangle formed by the three parallel lines through the three midpoints of sides of a triangle is called its medial triangle.