University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2021
Views:

55

Pages:

2
Author:

szkafut4kac

Name Key Date Section 9.4 A-Triangle Inequality Theorem Triangle Inequality Theorem The sum of the lengths of any two sides, of a triangle is length of the third side. 2 smallest sides greater than the Example: Determine if the given side lengths form a triangle. a) 4, 5, 10 b) 4,5,9 c) 4, 5, 7 4 + 5 > 10 9710 no 4 + 5 > 9 979 no 4+577 977 yes Practice: The triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Using this theorem, answer the following questions. 1) If two sides of a triangle are 1 and 3, the third side may be: (a) 5 14375 4 * 5 no (b) 2 1+273 373 no ((c) 3 i + 3 > 3 473 Yes (d) 4 1 + 3 > 4 474 2) If the lengths of two sides of a triangle are 5 and 7, the length of the third side may not be: a) 12 5 + 7 > 12 12712 no (b) 7 5 + 7 > 7 1277 yes (c) 3 3 + 5 > 7 aligned 8>7\\ y e5 aligned (d) 5 5+577 1077 yes Name: Date 3) Which set of numbers may represent the lengths of the sides of a triangle? (a) (2,5,9) (b) (6,6,7) (c) (6,4,2) (d) (7,8,1) 2+579 779 no 6 + 6 > 7 1277 yes 2 + 4 > 6 676 no 1 + 7 > 8 878 no 4) If the lengths of two sides of a triangle are 4 and 10, which could be the length of the third side? (a) 6 (b) 8 (c) 14 (d) 16 4+6710 10710 4+8710 12710 ves 4 + 10 > 14 14 14 no 4 + 10 > 16 14716 no 5) If the lengths of two sides of a triangle measure 7 and 12, the length of the third side could measure: (a)16 7 + 12 > 16 19716 ves (b) 19 712719 19719 no (c) 3 3 + 7 > 12 10712 no (d) 5 5 + 7 > 12 12712 no 6) Two sides of an isosceles triangle have lengths 2 and 12, respectively. Find the length of the third side. 2 12 2+2712 4712 no 2 + 12 > 12 14712 yes 12 3rd sicle 2 or 12 7) If the lengths of two sides of a triangle are 10 and 14, the length of the third side may be: (a) 22 10114222 24722 (b) 2 2 +|0714 12714 (c) 24 10 + 14 > 241 24724 (d) 4 4110714 14714 no A