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NAME ______DATE______PERIOD ______

Chapter 5, section 5: TRIANGLE INEQUALITIES Sides Could a Classify by Sum of >, <, or Larger triangle be Sides shorter = side (Scalene, Isosceles, made: Equilateral) sides Yes or No? 2 2 2 2 2 3 2 3 4 2 3 5 2 3 6 3 4 5 3 3 6 3 3 3 3 3 4 3 5 6

What did you find out? Triangle Inequality Theorem In order for a triangle to be constructed, the sum of any 2 sides must be ______the 3rd side. EXAMPLES: Determine if the following sides will make a triangle and if yes, then classify by sides. (Scalene, Isosceles, Equilateral) 1. 8, 9, 10 yes or no ______2. 1, 1, 2 yes or no ______3. 6, 6, 10 yes or no ______4. 3, 5, 7 yes or no ______5. 4, 4, 4 yes or no ______

*****In a triangle the largest side is opposite the largest angle, and the smallest side is opposite the smallest angle.

EXAMPLE 6:  A = 120,  B = 40, C = 20

B Largest side:

C Smallest side: A

EXAMPLE 7 Classify the triangle by sides, then list the angles from small to large.

12 B 70 Classify:______A 70

9 15 Angles:______, ______, ______

C

EXAMPLE 8 List the sides of ABC in order from longest to shortest if the angles of ABC have the indicated measures: mA = (10x), mB = (5x – 17), mC = (7x –1)° TRIANGLE INEQUALITY PROPERTIES Is it possible for a triangle to have sides with the following lengths? If YES, classify the triangle by its sides.

1. YES or NO Side lengths: 20, 9, 8

Classification:______

2. YES or NO Side lengths: 3, 4, 5

Classification:______

3. YES or NO Side lengths: 9, 12, 15

Classification:______

4. YES or NO Side lengths: 6, 6, 20

Classification:______

5. YES or NO Side lengths: 15, 15, 0.03

Classification:______

6. YES or NO Side lengths: 5, 5, 10.2

Classification:______

Name the longest segment in each of the following triangles.

7. ______A 70 C

65 B 8. ______A C

36 B A 9. ______

40 40 B C

10. ______A

10 150 B C Name the largest angle in each of the following.

11. ______3 11 13

1 2 12

12. ______3 x + 2

x 2

1 x + 4

List the sides of ∆ABC in order from longest to shortest if the angles of ∆ABC have the indicated measures.

13. Sides: m A = (5x + 2) ° , m B = (6x – 10) ° , and m C = (x + 20) ° .

14. Sides: m A = (x + 16) ° , m B = (x) ° , and m  C = (x + 29) ° .

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