Midsegments of Midsegments of Triangles and TrapezoidsTriangles and Trapezoids
Theorems, Postulates, & Definitions
Midsegment of a Triangle: A midsegment of a triangle is a segment whose endpoints are the midpoints of two sides.
Midsegment of a Trapezoid: A midsegment of a trapezoid is a segment whose endpoints are the midpoints of the nonparallel sides.
Midsegment TheoremMidsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as the sum of the length of the top and the bottom.
( )+ B
The length of the support ST is 23 inches.
∆ Midsegment Thm.
Substitute 46 for PQ.
Simplify.ST = 23
In an A-frame support, the distance PQ is 46 inches. What is the length of the support ST if S and T are at the midpoints of the sides?
( + 0)
The diagram shows an illustration of a roof truss, where UV and VW are midsegments of RST. Find UV and RS.
UV = ½(RT + S)
UV = ½(90 + 0)
UV = 45
45 in.
57 = ½(SR + 0)
VW = ½(SR + T)
57 = ½SR
114 = SR
114 in.
Find the value ofFind the value of n. n.
n + 14 = ½(3n + 12 + 0)
n + 14 = ½(3n + 12)
2(n + 14) = 2(½(3n + 12))
2n + 28 = 3n + 12
-1n = -16n = 16
3060
MidsegmentMidsegmentA midsegmentmidsegment of a triangle is a segment that
connects the midpoints of two sides of the triangle. Every triangle has 3 midsegments.
MidsegmentsMidsegments The midsegments of a triangle divide the triangle into 4 congruent triangles
In ∆XYZ, M, N, and P are midpoints.
The perimeter of ∆ MNP is 60. Find NP and YZ.
NP + MN + MP = 60 Definition of perimeter
Because the perimeter of MNP is 60, you can find NP.
Use the Triangle Midsegment Theorem to find YZ.
NP + 24 + 22 = 60 Substitute 24 for MN and 22 for MP.NP + 46 = 60 Simplify.
MP = (YZ + X) Triangle Midsegment Theorem12
22 = (YZ + 0) Substitute 22 for MP.12
44 = YZ Multiply each side by 2.
NP = 14 Subtract 46 from each side.
14
1. ED
2. AB
3. mBFE
10
14
Find each measure.Find each measure.
44° Corresponding Angles
∆XYZ is the midsegment triangle of
∆WUV. What is the perimeter of ∆XYZ?
4.5 + 4 + 3 = 11.5
1. XY
2. VW
3. XZ
4. Perimeter
8
4
44.5
4.5
Cases with more than one Parallel LineCases with more than one Parallel Line
Difference of the Bases divided by the number of spaces.
40
40
60 – 0 = 60
0
60
Difference of Bases20
20
Number of Spaces
30 – 10 = 20
15
15
20
20
25
25
16x22
7x55x3
1
16x2
2
12x8
8x + 12 = 2(2x + 16)
8x + 12 = 4x + 32
4x = 20
x = 5
EF = 26
a.a. b.b. c.c.x = 9x = 9 x = 14x = 14 x = 11x = 11
d.d. e.e. f.f.x = 23.5x = 23.5 x = 7x = 7 x = 2x = 2
Solve For The Variable in a – f.
g.g. = 40= 40 h.h. = 50= 50
i.i. = 160= 160 j.j. = 80= 80
Solve For The Variable
x.x. y.y.x = 6x = 6 y = 6.5y = 6.5
Assignment
3.7A and 3.7B3.7A and 3.7BSection 10 - 16Section 10 - 16