3.7 Midsegments of Triangles and Trapezoids

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3.7Midsegments of Triangles and Trapezoids

• Date ______________

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Midsegment of a Triangle
segment whose endpoints are the midpoints of two
sides of the triangle
Midsegment
Base
Midsegment ½ of Base
M ½ b
3
Find the length of the midsegment.
M ½ b
23
M ½ 46
46
M 23
4
Find the length of the base.
M ½ b
46
46 ½ b
2
2
92
92 b
5
Find the length of the midsegment and the base.
53-1
14
M ½ b
5x - 1 ½(6x 10)
5x - 1
5x - 1 3x 5
6x 10
-3x -3x
2x - 1 5
6310
28
1 1
2x 6
2 2
x 3
6
Midsegment of a Trapezoid
segment whose endpoints are the midpoints of
nonparallel sides.
Base 1
Midsegment
Base 2
Midsegment ½ (Sum of Bases)
M ½ (b1 b2)
7
Find the length of the midsegment.
42
M ½ (b1 b2)
M ½ (42 78)
60
M ½ (120)
78
M 60
8
Find the length of the missing base.
M ½(b1 b2)
6
42 ½(b1 78)
42 ½b1 39
42
-39 -39
3 ½ b1
2
2
78
6 b1
9
Find the length of the midsegment and the bases
of the trapezoid.
20
M ½(b1 b2)
355
3x 5
2x 16 ½(3x 5 5x 7)
26
2516
2x 16 ½(8x 12)
2x 16
2x 16 4x 6
557
32
-2x -2x
5x 7
16 2x 6
-6 -6
10 2x
2 2
5 x