Geometry

1
Geometry The Triangle Midsegment Theorem
2
Warm up
Find each length. 1) NX 2) MR 3) NP
P
1)
R
S
3
X
4.5
5.5
M
Q
N
3
The Triangle Midsegment Theorem
A midsegment of a triangle is a segment that
joins the midpoints of two sides of the triangle.
Every triangle has three midsegment, which form
the midsegment triangle.
Q
Y
X
P
R
Z
4
Examining Midsegments in the coordinate Plane
y
H(-5, 6)
6
L
4
J(1, 2)
K
2
0
x
-2
-2
G(-7, -2)
Next Page
5
y
H(-5, 6)
6
L
4
J(1, 2)
K
2
0
x
-2
-2
G(-7, -2)
Next Page
6
y
H(-5, 6)
6
L
4
J(1, 2)
K
2
0
x
-2
-2
G(-7, -2)
7
Now you try!
8
The relationship show in Example 1 is true for
the three midsegments of every triangle .
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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.
10
Using the triangle Midsegment Theorem
Find each measure.
S
U
A) UW
5.2
R
41
? Midsegment Thm. Substitute 7.4 for ST. Simplify.
V
7.4
W
T
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11
S
B) m/ SVU
U
5.2
R
41
V
7.4
? Midsegment Thm. Alt. Int. /s Thm. Substitute
41 for m/ VUW.
W
T
12
Now you try!
2) Find each measure. a) JL b) PM
c) m/ MLK
P
K
J
36
102
M
N
97
L
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Indirect Measurement Application
Anna wants to find the distance across the base
of Capulin Volcano, an extinct volcano in New
Mexico. She measures a triangle at one side of
the volcano as shown in the diagram. What is AE?
C
? midsegment Thm. Substitute 775 foe BD. Multiply
both sides by 2.
920 m
700 m
775 m
B
D
920 m
700 m
E
A
The distance AE across the base of the volcano is
about 1550 meters.
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Now you try!
3) Suppose Annas result in Example 3 is correct
to check it, she measures a second triangle. How
many meters will she measure between H and F?
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Now some problems for you to practice !
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Assessment
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• Find each measure.
• 2) NM 3) XZ
• 4) NZ 5) m/ LMN
• 6) m/ YXZ 7) m/ XLM

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8) In this A-frame house, the width of the first
floor XZ is 30 feet. The second floor CD is
slightly above and parallel to the midsegment of
?XYZ. Is the width of the second floor more or
less than 5 yards? Explain.
Y
C
D
X
Z
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Lets review
The Triangle Midsegment Theorem
A midsegment of a triangle is a segment that
joins the midpoints of two sides of the triangle.
Every triangle has three midsegment, which form
the midsegment triangle.
Q
Y
X
P
R
Z
20
Examining Midsegments in the coordinate Plane
y
H(-5, 6)
6
L
4
J(1, 2)
K
2
0
x
-2
-2
G(-7, -2)
Next Page
21
y
H(-5, 6)
6
L
4
J(1, 2)
K
2
0
x
-2
-2
G(-7, -2)
Next Page
22
y
H(-5, 6)
6
L
4
J(1, 2)
K
2
0
x
-2
-2
G(-7, -2)
23
The relationship show in Example 1 is true for
the three midsegments of every triangle .
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Theorem 4.1
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.
B
D
E
A
C
25
Using the triangle Midsegment Theorem
Find each measure.
S
U
A) UW
5.2
R
41
? Midsegment Thm. Substitute 7.4 for ST. Simplify.
V
7.4
W
T
Next Page
26
S
B) m/ SVU
U
5.2
R
41
V
7.4
? Midsegment Thm. Alt. Int. /s Thm. Substitute
41 for m/ VUW.
W
T
27
Indirect Measurement Application
Anna wants to find the distance across the base
of Capulin Volcano, an extinct volcano in New
Mexico. She measures a triangle at one side of
the volcano as shown in the diagram. What is AE?
C
? midsegment Thm. Substitute 775 foe BD. Multiply
both sides by 2.
920 m
700 m
775 m
B
D
920 m
700 m
E
The distance AE across the base of the volcano is
about 1550 meters.
A
28
You did a great job today!