Midsegment Theorem

Midsegment Theorem

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

Definition

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

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

Midpoint formula

Theorem

1. The midsegment and the opposite side are parallel. 2. [midsegment] = (1/2)[opposite side]

The midsegment theorem says that
the midsegment has two properties.

1. The midsegment and the opposite side
are parallel.

2. [midsegment] = (1/2)[opposite side]

Example

Find the value of x. [midsegment] = x, [opposite side] = 12

The blue segment
connects the midpoints of two sides.

So the blue segment
is the midsegment of the given triangle.

(midsegment) = x
(opposite side) = 12

So, by the midsegment theorem,
x = (1/2)⋅12.

(1/2)⋅12 = 6

So x = 6.