Midsegment
Theorem
Section 5.4
Definition

Midsegment of a triangle – a segment
that connects the midpoints of two sides
of a triangle.
How many
midsegments
does a triangle
have?
The
midsegments of
a triangle are
not concurrent.
Midsegment Theorem

The segment connecting the midpoints of two
sides of a triangle is parallel to the third side
and half as long.
C
DE
AB and
1
DE = (AB)
2
D
A
E
B
Example 1
UW and VW are midsegments of
RST. Find UW and RT.
R
UW = ½ (RS)
UW = 6
U
12
V
T
8
W
S
RT = 2(VW)
RT = 16
Example 2
If QP = 12, find QS.
Q
U
R
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T
P
Example 3
If QU = 24, find QR.
Q
U
R
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T
P
Example 4
If ST = 18, find QU.
Q
U
R
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T
P
Example 5
If RT = 3x + 6 and TP = 6x - 9,
find RT.
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U
R
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T
P
Example 6
If US = x + 6 and RP = 3x - 2,
find RT.
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Example 7
Given PQ = 14, SU = 6, and QU = 3,
find the perimeter of triangle STU.
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U
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Example 8
Given PS = 12, SU = 8, and QU = 4,
find the perimeter of triangle QRP.
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U
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Example 9
Given m∟QUS = 102o,
find m∟QRP.
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Example 10
If m∟QUS = (2x + 12)o and
m∟QRP = (4x – 6)o, find x.
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U
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P