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Triangle Midsegment Theorem


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 A B ¯ and E is the midpoint of A C ¯ .

So, D E ¯ 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 A D = D B and A E = E C ,

then D E ¯ B C ¯ and D E = 1 2 B C .

Example :

Find the value of x .

Here P is the midpoint of A B , and Q is the midpoint of B C . So, P Q ¯ is a midsegment.

Therefore by the Triangle Midsegment Theorem,

P Q = 1 2 B C


x = 1 2 6 = 3

The value of x is 3 .