The midsegment theorem states that a midsegment of a triangle, which is a segment that joins the midpoints of two sides, is parallel to the opposite side and its length is half the length of that side. The document provides examples of using the midsegment theorem to find lengths of midsegments and measure of angles related to midsegments. It defines a midsegment and illustrates it in diagrams of triangles.

1. 4.10.3 Triangle Midsegment Theorem
The student is able to (I can):
• Identify a midsegment of a triangle and use it to solve
problems.

2. midsegment A segment that joins the midpoints of two
sides of a triangle.
H
O
T
I C
E
Points I, C, and E are
midpoints of ∆HOT.
IC, CE, andEI
are midsegments.

3. Triangle Midsegment Theorem
A midsegment of a triangle is parallel to
a side of the triangle, and its length is
half the length of that side.
H
O
T
I C
E
1
IC HT,IC HT
2
=

4. Examples Find each measure.
1. FE
FE = 2(LT) = 2(14)
= 28
2. m∠UFE
m∠UFE = m∠TSE
= 62º
3. UE
UE = 2(9) = 18
F
L
U
T
E
S
14141414
62º62º62º62º
LT and TS
are midsegments.
9