Pre-Calculus Homework Solutions 143

Pre-Calculus Homework Solutions 143 - 14. In ABO and CBO,...

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145 Chapter 5 14. In n ABO and n CBO , A w B w > C w B w , O w B w > O w B w , and m / CBO , m / ABO .The SAS Inequality allows us to conclude that OC , OA . 15. In n ABC , A w B w > C w B w so n ABC is isosceles with base angles of measure } 1 2 } [180 2 (40 1 60)] or 40. m / AOB 5 ¬ 180 2 ( m / OAB 1 m / ABO ) 5 ¬ 180 2 (40 1 60) 5 ¬ 80 m / AOD 5 ¬ 180 2 m / AOB 5 ¬ 100 Therefore, m / AOD . m / AOB . 16. By the SAS Inequality, 10 , 3 x 2 2. 10 ¬ , 3 x 2 2 12 ¬ , 3 x 4 ¬ , x or x . 4 17. The triangle on the left is equilateral, so all angles have measure 60. Then by the SAS inequality, x 1 2 . 2 x 2 8. x 1 2 ¬ . 2 x 2 8 2 ¬ . x 2 8 10 ¬ . x The measure of any side is always greater than 0. 2 x 2 8 ¬ . 0 2 x ¬ . 8 x ¬ . 4 The two inequalities can be written as the compound inequality 4 , x , 10. 18. M w C w > M w C w , so by the SSS Inequality m / 1 . m / 2. 5 x 1 20 ¬ . 8 x 2 100 20 ¬ . 3 x 2 100 120 ¬ . 3 x 40 ¬ . x The measure of any angle is always greater than 0. 8 x 2 100 ¬ . 0 8 x ¬ . 100 x ¬ . 12.5 The two inequalities can be written as the compound inequality 12.5 , x , 40. 19. / RTV > / TRV , so n RVT is isosceles and R w V w > T w V w . S w V w > S w V w and RS , ST , so by the SSS Inequality, m / RVS , m / SVT . 15 1 5 x ¬ , 10 x 2 20 15 ¬ , 5 x 2 20 35 ¬ , 5 x 7 ¬ , x The measure of
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