1. The Triangle Midsegment Theorem
Geometry
The Triangle Midsegment Theorem
CONFIDENTIAL

2. Warm up Find each length. 1) NX 2) MR 3) NP P 1) S 3 R X 4.5 5.5 M Q N
CONFIDENTIAL

3. The Triangle Midsegment Theorem
A midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegment, which form the midsegment triangle. Q Y X P R Z
CONFIDENTIAL

4. Examining Midsegments in the coordinate Planey
H(-5, 6) 6 L 4
J(1, 2) K 2 x -2 -2
G(-7, -2)
Next Page:
CONFIDENTIAL

5. y
H(-5, 6) 6 L 4
J(1, 2) K 2 x -2 -2
G(-7, -2)
Next Page:
CONFIDENTIAL

6. y
H(-5, 6) 6 L 4
J(1, 2) K 2 x -2 -2
G(-7, -2)
CONFIDENTIAL

7. Now you try!
CONFIDENTIAL

8. The relationship show in Example 1 is true for the three midsegments of every triangle .
CONFIDENTIAL

9. Triangle Midsegment Theorem
A Midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side. B A D E C
CONFIDENTIAL

10. Using the triangle Midsegment Theorem
Find each measure. S U
A) UW
5.2 R
41˚
∆ Midsegment Thm.
Substitute 7.4 for ST.
Simplify. V
7.4 W T
Next Page:
CONFIDENTIAL

11. S B) m/ SVU U 5.2 R 41˚ V 7.4 ∆ Midsegment Thm. Alt. Int. /s Thm.
Substitute 41˚ for m/ VUW. W T
CONFIDENTIAL

12. Now you try! 2) Find each measure. a) JL b) PM c) m/ MLK P K J 36 102˚97 L
CONFIDENTIAL

13. Indirect Measurement Application
Anna wants to find the distance across the base of Capulin Volcano, an extinct volcano in New Mexico. She measures a triangle at one side of the volcano as shown in the diagram. What is AE? C
∆ midsegment Thm.
Substitute 775 foe BD.
Multiply both sides by 2.
920 m
700 m
775 m B D
920 m
700 m E A
The distance AE across the base of the volcano is about 1550 meters.
CONFIDENTIAL

14. Now you try!
3) Suppose Anna’s result in Example 3 is correct to check it, she measures a second triangle. How many meters will she measure between H and F? H F A E G
640 m
1005 m
CONFIDENTIAL

15. Now some problems for you to practice !
CONFIDENTIAL

16. Assessment
CONFIDENTIAL

17. Find each measure. 2) NM 3) XZ 4) NZ 5) m/ LMN 6) m/ YXZ 7) m/ XLM Y
10.2
5.6
29˚
CONFIDENTIAL

18. 8) In this A-frame house, the width of the first floor XZ is
30 feet. The second floor CD is slightly above and parallel
to the midsegment of ∆XYZ. Is the width of the second
floor more or less than 5 yards? Explain. Y C D X Z
CONFIDENTIAL

19. The Triangle Midsegment Theorem
Let’s review
The Triangle Midsegment Theorem
A midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegment, which form the midsegment triangle. Q Y X P R Z
CONFIDENTIAL

20. Examining Midsegments in the coordinate Planey
H(-5, 6) 6 L 4
J(1, 2) K 2 x -2 -2
G(-7, -2)
Next Page:
CONFIDENTIAL

21. y
H(-5, 6) 6 L 4
J(1, 2) K 2 x -2 -2
G(-7, -2)
Next Page:
CONFIDENTIAL

22. y
H(-5, 6) 6 L 4
J(1, 2) K 2 x -2 -2
G(-7, -2)
CONFIDENTIAL

23. The relationship show in Example 1 is true for the three midsegments of every triangle .
CONFIDENTIAL

24. Triangle Midsegment Theorem
A Midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side. B D E A C
CONFIDENTIAL

25. Using the triangle Midsegment Theorem
Find each measure. S U
A) UW
5.2 R
41˚
∆ Midsegment Thm.
Substitute 7.4 for ST.
Simplify. V
7.4 W T
Next Page:
CONFIDENTIAL

26. S B) m/ SVU U 5.2 R 41˚ V 7.4 ∆ Midsegment Thm. Alt. Int. /s Thm.
Substitute 41˚ for m/ VUW. W T
CONFIDENTIAL

27. Indirect Measurement Application
Anna wants to find the distance across the base of Capulin Volcano, an extinct volcano in New Mexico. She measures a triangle at one side of the volcano as shown in the diagram. What is AE? C
∆ midsegment Thm.
Substitute 775 foe BD.
Multiply both sides by 2.
920 m
700 m
775 m B D
920 m
700 m E
The distance AE across the base of the volcano is about 1550 meters. A
CONFIDENTIAL

28. You did a great job today!
CONFIDENTIAL