Download 5-1 Midsegments of Triangles

Midsegments of Triangles
LESSON 5-1
Additional Examples
In XYZ, M, N, and P are midpoints. The
perimeter of MNP is 60. Find NP and YZ.
Because the perimeter of
NP + MN + MP = 60
NP + 24 + 22 = 60
NP + 46 = 60
NP = 14
MNP is 60, you can find NP.
Definition of perimeter
Substitute 24 for MN and 22 for MP.
Simplify.
Subtract 46 from each side.
Use the Triangle Midsegment Theorem to find YZ.
MP = 1 YZ
Triangle Midsegment Theorem
2
22 = 1YZ
2
Substitute 22 for MP.
44 = YZ
Multiply each side by 2.
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HELP
GEOMETRY
Midsegments of Triangles
LESSON 5-1
Additional Examples
Find m
AMN and m
ANM.
MN and BC are cut by transversal AB , so
B are corresponding angles.
AMN and
MN || BC by the Triangle Midsegment Theorem, so
AMN
B because parallel lines cut by a transversal
form congruent corresponding angles.
m AMN = 75 because congruent angles have the
same measure.
In AMN, AM = AN, so m
Triangle Theorem.
m
ANM = m
ANM = 75 by substituting 75 for m
AMN by the Isosceles
AMN.
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HELP
GEOMETRY
Midsegments of Triangles
LESSON 5-1
Additional Examples
Explain why Dean could use the Triangle Midsegment
Theorem to measure the length of the lake.
Solution: To find the length of the lake, Dean starts at the end of
the lake and paces straight along that end of the lake. He counts
the number of strides (35). Where the lake ends, he sets a stake.
He paces the same number of strides (35) in the same direction and
sets another stake. The first stake marks the midpoint of one side
of a triangle.
Dean paces from the second stake straight to the other end of the lake.
He counts the number of his strides (236).
HELP
GEOMETRY
Midsegments of Triangles
LESSON 5-1
Additional Examples
(continued)
Dean finds the midsegment of the second side by pacing exactly half
the number of strides back toward the second stake. He paces 118
strides. From this midpoint of the second side of the triangle, he
returns to the midpoint of the first side, counting the number of
strides (128). Dean has paced a triangle. He has also formed a
midsegment of a triangle whose third side is the length of the lake.
By the Triangle Midsegment Theorem, the segment connecting
the two midpoints is half the distance across the lake. So, Dean
multiplies the length of the midsegment by 2 to find the length of
the lake.
HELP
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GEOMETRY