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 AB ¯ and E is the midpoint of AC ¯ .

So, 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=DBandAE=EC,

then DE ¯ BC ¯ and DE= 1 2 BC .

Example :

Find the value of x .

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

Therefore by the Triangle Midsegment Theorem,

PQ= 1 2 BC

Substitute.

x= 1 2 6 =3

The value of x is 3 .