What is midpoint theorem?

The midpoint theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side. In other words, if you have a triangle ABC and D is the midpoint of side AB, and E is the midpoint of side AC, then DE is parallel to BC and DE = 1/2 BC.

The midpoint theorem can be proved using similar triangles. By drawing lines to create two smaller triangles inside the larger triangle, it can be shown that the smaller triangles are similar to the larger triangle and that the sides are proportional, leading to the conclusion that the line connecting the midpoints is parallel to the third side and is half its length.

The midpoint theorem is a useful tool in geometry for solving problems involving triangles, such as finding missing side lengths or angles. It is also an important concept in coordinate geometry, where the midpoint formula can be used to find the midpoint of a line segment.