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Section 5-5The Triangle Inequality
Thursday, March 15, 2012
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?
Thursday, March 15, 2012
Exercise
Draw a triangle with the following side lengths:6 cm, 4 cm, and 10 cm
Thursday, March 15, 2012
Theorem 5.11 - Triangle Inequality Theorem
Thursday, March 15, 2012
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
Thursday, March 15, 2012
Example 1Is it possible to form a triangle with the given side lengths?
If not, explain why not.
a. 6
12
,612
,1412
b. 6.8, 7.2, 5.1
Thursday, March 15, 2012
Example 1Is it possible to form a triangle with the given side lengths?
If not, explain why not.
a. 6
12
,612
,1412
b. 6.8, 7.2, 5.1
No; 6
12+ 6
12<14
12
Thursday, March 15, 2012
Example 1Is it possible to form a triangle with the given side lengths?
If not, explain why not.
a. 6
12
,612
,1412
b. 6.8, 7.2, 5.1
No; 6
12+ 6
12<14
12
Yes
Thursday, March 15, 2012
Example 1Is it possible to form a triangle with the given side lengths?
If not, explain why not.
a. 6
12
,612
,1412
b. 6.8, 7.2, 5.1
No; 6
12+ 6
12<14
12
Yes
5.1 + 6.8 > 7.2
Thursday, March 15, 2012
Example 2In ∆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
Thursday, March 15, 2012
Example 2In ∆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 =
Thursday, March 15, 2012
Example 2In ∆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
Example 2In ∆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
Example 2In ∆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
Example 3The 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.
Thursday, March 15, 2012
Example 3The 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
Example 3The 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.
Thursday, March 15, 2012
Check Your Understanding
Look at #1-5 on page 362
Thursday, March 15, 2012
Problem Set
Thursday, March 15, 2012
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