1. Triangles and Trapezoids
3.7 Midsegments of
Triangles and Trapezoids

2. 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.
Homework

3. Homework Midsegment 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
Homework

4. Homework The length of the support ST is 23 inches.
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?
( )
∆ Midsegment Thm.
Substitute 46 for PQ.
ST = 23
Simplify.
The length of the support ST is 23 inches.
Homework

5. 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.
VW = ½(SR + T)
114 = SR
114 in.
57 = ½(SR + 0)
57 = ½SR
Homework

6. Homework Find the value of n. 60 30 n + 14 = ½(3n + 12 + 0)

7. Midsegment
A midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle. Every triangle has 3 midsegments.
Homework

8. Midsegments
The midsegments of a triangle divide the triangle into 4 congruent triangles
Homework

9. Homework The perimeter of ∆ MNP is 60. Find NP and YZ.
In ∆XYZ, M, N, and P are midpoints.
The perimeter of ∆ MNP is 60. Find NP and YZ.
NP = Subtract 46 from each side. 14
Because the perimeter of MNP is 60, you can find NP.
NP + MN + MP = 60 Definition of perimeter
NP = Substitute 24 for MN and 22 for MP.
NP + 46 = Simplify.
Use the Triangle Midsegment Theorem to find YZ.
MP = (YZ + X) Triangle Midsegment Theorem 1 2
22 = (YZ + 0) Substitute 22 for MP. 1 2
44 = YZ Multiply each side by 2.
Homework

10. Homework Find each measure. 1. ED 2. AB 10 3. mBFE 14
44° Corresponding Angles
1. ED
2. AB
3. mBFE 10 14
Homework

11. ∆XYZ is the midsegment triangle of ∆WUV. What is the perimeter of ∆XYZ?
4.5
1. XY
2. VW
3. XZ
4. Perimeter 4 8
= 11.5
Homework

12. Cases with more than one Parallel Line
Difference of the Bases divided by the number of spaces.
60 – 0 = 60 60
Difference of Bases
30 – 10 = 20 15 40 20 25 20
Number of
Spaces
Homework

13. 8x + 12 = 2(2x + 16)
8x + 12 = 4x + 32
4x = 20
x = 5
EF = 26
Homework

14. Solve For The Variable in a – f.
x = 9 b.
x = 14 c.
x = 11 d.
x = 23.5 e.
x = 7 f.
x = 2 g.
= 40 h.
= 50 i.
= 160 j.
= 80
Homework

15. Solve For The Variable x.
x = 6 y.
y = 6.5
Homework

16. Assignment
3.7A and 3.7B
Section