Geometry Section 5-5 1112
-
Upload
jimbo-lamb -
Category
Education
-
view
1.100 -
download
1
description
Transcript of Geometry Section 5-5 1112
![Page 1: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/1.jpg)
Section 5-5The Triangle Inequality
Thursday, March 15, 2012
![Page 2: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/2.jpg)
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
![Page 3: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/3.jpg)
Exercise
Draw a triangle with the following side lengths:6 cm, 4 cm, and 10 cm
Thursday, March 15, 2012
![Page 4: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/4.jpg)
Theorem 5.11 - Triangle Inequality Theorem
Thursday, March 15, 2012
![Page 5: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/5.jpg)
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
![Page 6: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/6.jpg)
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
![Page 7: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/7.jpg)
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
![Page 8: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/8.jpg)
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
![Page 9: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/9.jpg)
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
![Page 10: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/10.jpg)
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
![Page 11: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/11.jpg)
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
![Page 12: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/12.jpg)
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
![Page 13: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/13.jpg)
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
![Page 14: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/14.jpg)
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
![Page 15: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/15.jpg)
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
![Page 16: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/16.jpg)
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
![Page 17: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/17.jpg)
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
![Page 18: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/18.jpg)
Check Your Understanding
Look at #1-5 on page 362
Thursday, March 15, 2012
![Page 19: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/19.jpg)
Problem Set
Thursday, March 15, 2012
![Page 20: Geometry Section 5-5 1112](https://reader031.fdocuments.net/reader031/viewer/2022020217/547c6b33b47959b1508b4661/html5/thumbnails/20.jpg)
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