<p>NAME ______DATE______PERIOD ______</p><p>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</p><p>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 ______</p><p>*****In a triangle the largest side is opposite the largest angle, and the smallest side is opposite the smallest angle.</p><p>EXAMPLE 6:  A = 120,  B = 40, C = 20</p><p>B Largest side: </p><p>C Smallest side: A </p><p>EXAMPLE 7 Classify the triangle by sides, then list the angles from small to large.</p><p>12 B 70 Classify:______A 70</p><p>9 15 Angles:______, ______, ______</p><p>C</p><p>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.</p><p>1. YES or NO Side lengths: 20, 9, 8</p><p>Classification:______</p><p>2. YES or NO Side lengths: 3, 4, 5</p><p>Classification:______</p><p>3. YES or NO Side lengths: 9, 12, 15</p><p>Classification:______</p><p>4. YES or NO Side lengths: 6, 6, 20</p><p>Classification:______</p><p>5. YES or NO Side lengths: 15, 15, 0.03</p><p>Classification:______</p><p>6. YES or NO Side lengths: 5, 5, 10.2</p><p>Classification:______</p><p>Name the longest segment in each of the following triangles.</p><p>7. ______A 70 C</p><p>65 B 8. ______A C</p><p>36 B A 9. ______</p><p>40 40 B C</p><p>10. ______A</p><p>10 150 B C Name the largest angle in each of the following.</p><p>11. ______3 11 13</p><p>1 2 12</p><p>12. ______3 x + 2</p><p> x 2</p><p>1 x + 4</p><p>List the sides of ∆ABC in order from longest to shortest if the angles of ∆ABC have the indicated measures.</p><p>13. Sides: m A = (5x + 2) ° , m B = (6x – 10) ° , and m C = (x + 20) ° .</p><p>14. Sides: m A = (x + 16) ° , m B = (x) ° , and m  C = (x + 29) ° .</p>