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Triangle Midsegment Theorem

Midsegment

In the figure $D$ is the midpoint of $\overline{AB}$ and $E$ is the midpoint of $\overline{AC}$ .

So, $\overline{DE}$ is a midsegment.

The Triangle Midsegment Theorem

A midsegment connecting two sides of a triangle is parallel to the third side and is half as long.

If $AD=DB\text{and}AE=EC,$

then $\overline{DE}\parallel \overline{BC}$ and $DE=\frac{1}{2}BC$ .