The document discusses triangle midsegments. A midsegment is a segment that joins the midpoints of two sides of a triangle. The Triangle Midsegment Theorem states that a midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side. Examples are provided to demonstrate using the theorem to find the measures of lengths and angles associated with midsegments in triangles.

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

2. midsegmentmidsegmentmidsegmentmidsegment –––– 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 ΔHOT.
, ,andIC CE EI
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
,
2
IC HT HT=IC

4. Examples Find each measure.
1. FE
2. m∠UFE
3. UE
F
L
U
T
E
S
14141414
62626262°°°°
andLT TS
are midsegments.
9

5. Examples Find each measure.
1. FE
FE = 2(LT) = 2(14)
= 28
2. m∠UFE
m∠UFE = m∠TSE
= 62°
3. UE
UE = 2(9) = 18
F
L
U
T
E
S
14141414
62626262°°°°
andLT TS
are midsegments.
9