1. Midsegment Theorem

2. Vocabulary
The Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle. D B C E A
D and E are midpoints
DE is the midsegment

3. Theorem 5.1 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 that side. D B C E A

4. Example 1
In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU.
5 ft
16 ft
TU = ________
PR = ________

5. Example 2
In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY.
14 cm
53 cm
ZY = ________
MN = ________

6. Example 3
In the diagram, ED and DF are midsegments of triangle ABC. Find DF and AB.
3X - 4
5X+2
x = ________ 10
DF = ________ 26
AB = ________ 52