Midpoint theorem (triangle)
The midpoint theorem (also known as the midsegment theorem) states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and is half the length of that side.
More formally:
Given a triangle ABC, if D is the midpoint of AB and E is the midpoint of AC, then:
- DE is parallel to BC (DE || BC).
- DE = (1/2) BC.
The converse of the midpoint theorem is also true: If a line segment drawn from the midpoint of one side of a triangle is parallel to another side, then it bisects the third side. Specifically, given triangle ABC, if D is the midpoint of AB and DE || BC, then E is the midpoint of AC.