1. Honors Geometry

2. Relationships in Triangles
Chapter 5
Relationships in Triangles

3. The Triangle Inequality
Section 5-5
 The Triangle Inequality
Objective:
To use the Triangle Inequality Theorem to identify possible triangles
To prove triangles relationships using the Triangle Inequality Theorem.

4. Theorem 5.11: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Given: ΔABC Prove: (1) AB + BC > AC (2) AB + AC > BC (3) AC + BC > AB C A B
The Triangle Inequality Theorem can be used to determine whether three segments can form a triangle.

5. Example: Is it possible for a triangle to have sides with the lengths indicated below.
1.) 10, 9, 8
Yes
2.) 6, 6, 20 No
3.) 7, 7, 14.1 No
4.) 16, 11, 5 No
5.) 0.6, 0.5, 1
Yes
6.) 18, 18, 0.06
Yes

6. Example: Find the range for the measure of the third side of a triangle given the measures of two sides.
5, 7, n

7. n < 12 n > 2 n > -2 2 < n < 12 6 5 3 4 2 9 7 8 10 1 11-1 6 5 3 4 2 9 7 8 10 1 11 12 -2
n > 2 -1 6 5 3 4 2 9 7 8 10 1 11 12 -2
n > -2 -1 6 5 3 4 2 9 7 8 10 1 11 12 -2 -1
2 < n < 12

8. Example: Find the range for the measure of the third side of a triangle given the measures of two sides.
5, 7, n
2 < n < 12

9. 2 < n < 10 8 < n < 14 0 < n < 24 0 < n < 10
Example: Find the range for the measure of the third side of a triangle given the measures of two sides.
1.) 4 and 6
2 < n < 10
2.) 3 and 11
8 < n < 14
3.) 12 and 12
0 < n < 24
4.) 5 and 5
0 < n < 10

10. End of Section 5.5