1. 6.4 Triangle midsegment theorem

2. What We Will Learn Use midsegments in coordinate plane
Use midsegments to find distance

3. Needed Vocab
Midsegment: segment that contains the two midpoints of two sides of a triangle

4. Ex. 1 Showing a Midsegment
To be a midsegment, must be parallel to opposite side and half the length of the opposite side
Find slope of each
m(MN) = 3−2 −4−0 = 1 −4
m(JL) = −1−1 2−(−6) = −2 8 = −1 4
Find distance of each
d(MN) = −4− −2 2 −
16+1
17 ≈4.12
d(JL) = −6− −(−1) 2 −
64+4
68 ≈8.24

5. Ex. 3 Using Midsegment Thm.
Triangles are used for strength in roof trusses. In the diagram, UV and VW are midsegments of RST. Find UV and RS.
UV:
Half of RT 45
RS:
Twice as long as VW
114

6. Your Practice 2 3𝑥+8 =2𝑥+24 6𝑥+16=2𝑥+24 −2𝑥−16−2𝑥−16 4𝑥=8 4𝑥 4 = 8 4
A, B, and C are midpoints.
When AB = 3x + 8 and GJ = 2X + 24, what is AB?
Find x first, then plug back in
AB is midsegment of GJ, so AB is half of GJ.
Set up one of two ways:
2 3𝑥+8 =2𝑥+24 𝑜𝑟 3𝑥+8= 1 2 (2𝑥+24)
2 3𝑥+8 =2𝑥+24
6𝑥+16=2𝑥+24
−2𝑥−16−2𝑥−16
4𝑥=8
4𝑥 4 = 8 4
𝑥=2
AB =
6+8
AB = 14

7. Ex. 5 Using Diagrams
Pear Street intersects Cherry Street and Peach Street at their midpoints. Your home is at point P. You leave your home and jog down Cherry Street to Plum Street, over Plum Street to Peach Street, up Peach Street to Pear Street, over Pear Street to Cherry Street, and back home up Cherry Street. How many miles did you jog?
= miles