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.