# Midsegment Theorem

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

## Definition

The midsegment of a triangle

is a line segment

that connects the midpoints of two sides.

## 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

Solution

Solution (Detail)

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.