1. Inequalities in One Triangle
Section 5-5
Inequalities in One Triangle

2. Theorem 5-10
Longest sideLargest angle
Shortest side Smallest angle

3. Example: N D A 6 8 10

4. Theorem 5-11 (Converse) Largest angleLongest side
Smallest angleShortest side

5. Example: C A T
CT < TA < CA

6. Shortest Side: _________. Shortest Side: _________
Shortest Side: _________ Shortest Side: _________ Shortest Side: _________
Largest Side: _________ Largest Side: _________ Largest Side: _________

7. Smallest Angle: _________. Smallest Angle: _________
Smallest Angle: _________ Smallest Angle: _________ Smallest Angle: _________
Largest Angle: _________ Largest Angle: _________ Largest Angle: _________

9. List the sides from least to greatest
PN, PO, ON, NM, MO
55°
50°
75° P
55°
87°
38° N M

10. RECALL Exterior Angle TheoremB C 1

11. Exterior Angle Inequality Theorem
The measure of an exterior Angle is always greater than the measure of a non-adjacent angle

12. A B C 1

13. Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Side + Side > Largest Side

14. Example #1:
Is it possible for a triangle to have sides with the lengths as indicated?
a.) 6, 6, 5
b.) 3, 4, 8
c.) 2.5, 4.1, 5.0
Yes No
Yes

15. Practice Problems 5in, 2in, 8in. 6m, 12m, 15m 3ft, 2ft, 3 ft
50cm, 60cm, 111cm
1in, 1in, 2in

16. The lengths of two sides of a triangle are 8 and 10
The lengths of two sides of a triangle are 8 and 10. Then, the length of the third side must be greater than ______ but less than ______. 2 18
2<x<18

17. Practice Problems 7 and 12 7 and 8 9 and 15 12 and 13 5 and 5
Find possible measures for the 3rd segment of the triangle given side lengths:
7 and 12
7 and 8
9 and 15
12 and 13
5 and 5

18. More practice problems!!
Solve the inequality AB+AC>BC A
x x + 3 > 3x – 2
2x + 5 > 3x – 2
7 > x
x < 7
x + 2
x + 3 C B
3x - 2