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

2023
Views:

488

Pages:

2
Author:

nesikhiyawl0

TRIANGLE THEOREMS angle Theorem 1: If one side of a triangle is longer than a second side, then the ___________ opposite the first side is larger than the angle opposite the second side. largest • The longest side is opposite the __________________ angle. smallest • The shortest side is opposite the _________________ angle. Examples: Name the (a) smallest and (b) largest angles in the given triangles. C H D 1. smallest _____ 2. smallest _____ 3. smallest _____ B _____ largest largest F _____ D C 17 Theorem 2: • • 22 16 A I _____ H E B 15 largest 2x+15 10 F 20 G 2x I x side If one angle of a triangle is larger than a second angle, then the __________ opposite the first angle is longer than the side opposite the second angle. longest The largest angle is opposite the ___________________ side. shortest The smallest angle is opposite the __________________ side. Examples: Name the (a) shortest and (b) longest side for each triangle. AB 4. shortest _____ EF 5. shortest _____ HG 6. shortest _____ BC longest _____ DF longest _____ HI longest _____ B D 65 45 70 A C H E 36 54 F x 60 65 (x+5) 55 125 G I r.int + r.int = ext x + x + 5 = 125  2x = 120 X = 60 Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A In ABC, > AB + BC _____ AC, > AB + AC _____ BC, and C > AC + BC _____ AB. B THE SUM OF THE TWO SMALLEST S MUST To determine if the figure is a , ______________________________________ BE GREATER THAN THE LARGEST … SM + MED > LG ________________________________________________________________ Examples: Is it possible for a triangle to have sides with the lengths indicated? 1. 4, 8, 3 2. 3, 4, 5 3. 7, 6, 13 4+3?8 NOT >, NO  3+4?5 YES >,  7 + 6 ? 13 NOT >, NO  4. 9, 9, 5 5+9?9 YES >,  The lengths of the two sides of a triangle are given. Write the numbers that best complete the statement: The length of the third side must be (a) greater than ___, but (b) less than ___. 5. 5, 15 6. 10.5, 7.5 10 (15-5) (a) _____ 3 (10.5-7.5) (a) _____ 20 (15+5) (b) _____ 18 (10.5+7.5) (b) _____