The Triangle Ineq

1. Section 5-5
The Triangle Inequality
Thursday, March 15, 2012

2. Essential Questions
• How do you use the Triangle Inequality
Theorem to identify possible triangles?
• How do you prove triangle relationships
using the Triangle Inequality Theorem?
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3. Exercise
Draw a triangle with the following side lengths:
6 cm, 4 cm, and 10 cm
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4. Theorem 5.11 - Triangle
Inequality Theorem
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5. Theorem 5.11 - Triangle
Inequality Theorem
The sum of the lengths of any two sides of a triangle must
be greater than the length of the third side
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6. Example 1
Is it possible to form a triangle with the given side lengths?
If not, explain why not.
1 1 1
a. 6 , 6 ,14 b. 6.8, 7.2, 5.1
2 2 2
Thursday, March 15, 2012

7. Example 1
Is it possible to form a triangle with the given side lengths?
If not, explain why not.
1 1 1
a. 6 , 6 ,14 b. 6.8, 7.2, 5.1
2 2 2
1 1 1
No; 6 + 6 <14
2 2 2
Thursday, March 15, 2012

8. Example 1
Is it possible to form a triangle with the given side lengths?
If not, explain why not.
1 1 1
a. 6 , 6 ,14 b. 6.8, 7.2, 5.1
2 2 2
Yes
1 1 1
No; 6 + 6 <14
2 2 2
Thursday, March 15, 2012

9. Example 1
Is it possible to form a triangle with the given side lengths?
If not, explain why not.
1 1 1
a. 6 , 6 ,14 b. 6.8, 7.2, 5.1
2 2 2
Yes
1 1 1
No; 6 + 6 <14
2 2 2 5.1 + 6.8 > 7.2
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10. Example 2
In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following
measures cannot be AC? Why not?
a. 7 b. 9 c. 11 d. 13
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11. Example 2
In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following
measures cannot be AC? Why not?
a. 7 b. 9 c. 11 d. 13
7.2 + 5.2 =
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12. Example 2
In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following
measures cannot be AC? Why not?
a. 7 b. 9 c. 11 d. 13
7.2 + 5.2 = 12.4
Thursday, March 15, 2012

13. Example 2
In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following
measures cannot be AC? Why not?
a. 7 b. 9 c. 11 d. 13
7.2 + 5.2 = 12.4
So the third side must be less than 12.4
Thursday, March 15, 2012

14. Example 2
In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following
measures cannot be AC? Why not?
a. 7 b. 9 c. 11 d. 13
7.2 + 5.2 = 12.4
So the third side must be less than 12.4
d. 13 cannot be a measure for AC
Thursday, March 15, 2012

15. Example 3
The towns of Mitarnowskia, Fuzzy-Jeffington, and
Sheckyville are shown in the map below. Prove that by
driving from Mitarnowskia to Fuzzy-Jeffington and then
Fuzzy-Jeffington to Sheckyville is a greater distance than
driving from Mitarnowskia to Sheckyville.
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16. Example 3
The towns of Mitarnowskia, Fuzzy-Jeffington, and
Sheckyville are shown in the map below. Prove that by
driving from Mitarnowskia to Fuzzy-Jeffington and then
Fuzzy-Jeffington to Sheckyville is a greater distance than
driving from Mitarnowskia to Sheckyville.
Let the vertices be F, M, and S.
Thursday, March 15, 2012

17. Example 3
The towns of Mitarnowskia, Fuzzy-Jeffington, and
Sheckyville are shown in the map below. Prove that by
driving from Mitarnowskia to Fuzzy-Jeffington and then
Fuzzy-Jeffington to Sheckyville is a greater distance than
driving from Mitarnowskia to Sheckyville.
Let the vertices be F, M, and S.
By the Triangle Inequality
Theorem, MF + FS > MS.
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18. Check Your
Understanding
Look at #1-5 on page 362
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19. Problem Set
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20. Problem Set
p. 363 #7-33 odd, 43, 53, 57
"If you can find a path with no obstacles, it probably
doesn't lead anywhere." - Frank A. Clark
Thursday, March 15, 2012