Triangle Midsegment Theorem

Midsegment

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

In the figure D is the midpoint of and E is the midpoint of .

So, 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 and AE = EC,

then and

Example :

Find the value of x.

Here P is the midpoint of AB, and Q is the midpoint of BC. So, is a midsegment.

Therefore by the Triangle Midsegment Theorem,

Substitute.

The value of x is 3.