Midsegment Theorem

How to find the midsegment of a triangle by using the midsegment theorem: definition, theorem, 1 example, and its solution.

Definition

Definition

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

Theorem

Theorem

The midsegment has two properties.

The midsegment and the opposite side
are parallel.

The midsegment (m) and the opposite side (a)
satisfy this formula:
m = (1/2)a.

This is the midsegment theorem.

Example

Example

Solution

The blue segment connects
the midpoints of two sides.

So the blue segment is the midsegment.

The midsegment and the opposite side
are parallel.

The midsegment is x.
The opposite side is 12.
Then x = (1/2)⋅12.

(1/2)⋅12 = 6

So x = 6.