Pre-Calculus Homework Solutions 90

Pre-Calculus Homework Solutions 90 - 41 Given ABC Prove m...

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41. Given: n ABC Prove: m / CBD 5 m / A 1 m / C Proof: 42. Given: n RST / R is a right angle Prove: / S and / T are complementary Proof: 43. Given: n MNO / M is a right angle. Prove: There can be at most one right angle in a triangle. Proof: In n MNO , / M is a right angle. m / M 1 m / N 1 m / O 5 180. m / M 5 90, so m / N 1 m / O 5 90. If / N were a right angle, then m / O 5 0. But that is impossible, so there cannot be two right angles in a triangle. Given: n PQR / P is obtuse. Prove: There can be at most one obtuse angle in a triangle. Proof: In n PQR , / P is obtuse. So m / P . 90. m / P 1 m / Q 1 m / R 5 180. It must be that m / Q 1 m / R , 90. So, / Q and / R must be acute. 44. Given: / A > / D / B > / E Prove: / C > / F Proof: 45. m / 1 1 m / 2 1 m / 3 5 ¬ 180 4 x 1 5 x 1 6 x 5 ¬ 180 15 x 5 ¬ 180 x 5 ¬ 12 m / 1 5 4(12) or 48 m / 2 5 5(12) or 60 m / 3 5 6(12) or 72 46. Sample answer: The shape of a kite is symmetric. If triangles are used on one side of the kite, congruent triangles are used on the opposite side. The wings of this kite are made from congruent right triangles. Answers should include the following.
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.

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