1. Geometry
6.4 Midsegment Theorem

2. Geometry 5.4 Midsegment Theorem
Essential Question
What are the properties of the midsegments of a triangle?
January 2, 2019
Geometry 5.4 Midsegment Theorem

3. Geometry 6.4 Midsegment Theorem
January 2, 2019
Geometry 6.4 Midsegment Theorem

4. Triangle Midsegment Theorem (6.8)
January 2, 2019
Geometry 5.4 Midsegment Theorem

5. Using the midsegment properties
DE is a midsegment of ABC 12 ? 24
January 2, 2019
Geometry 5.4 Midsegment Theorem

6. Using the midsegment properties
DE is a midsegment of ABC 5 10 ?
January 2, 2019
Geometry 5.4 Midsegment Theorem

7. Geometry 5.4 Midsegment Theorem
Example 1: 6 ? 12
January 2, 2019
Geometry 5.4 Midsegment Theorem

8. Geometry 5.4 Midsegment Theorem
Example 1: 8 ? 6 4 12
January 2, 2019
Geometry 5.4 Midsegment Theorem

9. Geometry 5.4 Midsegment Theorem
Example 1: 10 8 6 5 ? 4 12
January 2, 2019
Geometry 5.4 Midsegment Theorem

10. Geometry 5.4 Midsegment Theorem
Example 1: 30
The perimeter of the outer triangle is_______. 10 8 6 5 4 12 15
The perimeter of the inner triangle is_______.
January 2, 2019
Geometry 5.4 Midsegment Theorem

11. Geometry 5.4 Midsegment Theorem
Example 2
DE is a midsegment of ABC
Solve for x.
DE = ½ AB
3x + 8 17
10x + 4 34
January 2, 2019
Geometry 5.4 Midsegment Theorem

12. Some Old, and Important, Formulas
Midpoint
Distance
Slope
January 2, 2019
Geometry 5.4 Midsegment Theorem

13. Geometry 5.4 Midsegment Theorem
Coordinate Geometry
On graph paper, draw RST
R(0,0) S(2, 6) T(8, 0)
Find M, the midpoint of RS.
(1, 3)
Find N, the midpoint of ST.
(5, 3)
Draw midsegment MN.
S(2, 6)
N(5, 3)
M(1, 3)
R(0, 0)
T(8, 0)
January 2, 2019
Geometry 5.4 Midsegment Theorem

14. Geometry 5.4 Midsegment Theorem
Coordinate Geometry
Verify that MN is parallel to RT.
Slope of MN
S(2, 6)
Slope of RT
N(5, 3)
M(1, 3)
R(0, 0)
T(8, 0)
Slopes are equal: Lines are parallel.
January 2, 2019
Geometry 5.4 Midsegment Theorem

15. Geometry 5.4 Midsegment Theorem
Coordinate Geometry
Verify that MN = ½ RT.
Length MN
S(2, 6)
Length RT
N(5, 3)
M(1, 3)
R(0, 0)
T(8, 0)
MN = ½ RT
January 2, 2019
Geometry 5.4 Midsegment Theorem

16. Geometry 5.4 Midsegment Theorem
Coordinate Geometry
The theorem is verified.
S(2, 6) 4
N(5, 3)
M(1, 3) 8
R(0, 0)
T(8, 0)
January 2, 2019
Geometry 5.4 Midsegment Theorem

17. Geometry 5.4 Midsegment Theorem
Summary
A midsegment (midline) of a triangle is the segment between the midpoints of two sides.
The midsegment is parallel to the third side.
The midsegment is half the length of the third side.
January 2, 2019
Geometry 5.4 Midsegment Theorem