Pre-Calculus Homework Solutions 107

Pre-Calculus Homework Solutions 107 - 32. Given: MNO is an...

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32. Given: n MNO is an equilateral triangle. Prove: m / M 5 m / N 5 m / O 5 60 Proof: 33. Given: n ABC / A > / C Prove: A w B w > C w B w Proof: 34. The minimum requirement is that two angles measure 60°. 35. The front face of the figure has two congruent angles and one angle of measure 60. Let y represent the measure of each of the congruent angles. y 1 y 1 60 5 ¬ 180 2 y 1 60 5 ¬ 180 2 y 5 ¬ 120 y 5 ¬ 60 Therefore all angles have measure 60, so the triangle is equiangular and equilateral. All sides have length 2 x 1 5, in particular the edge between the front face and the side face showing. Because the side face has two congruent base angles it is isosceles and the sides opposite the congruent angles are congruent. 2 x 1 5 5 ¬ 3 x 2 13 2 x 1 18 5 ¬ 3 x 18 5 ¬ x 36. The triangle is isosceles with base angles having measure 3 x 1 8. (3 x 1 8) 1 (3 x 1 8) 1 (2 x 1 20) 5 ¬ 180 8 x 1 36 5 ¬ 180 8 x 5 ¬ 144 x 5 ¬ 18 37. The triangle on the bottom half of the figure is isosceles. The base angles are congruent.
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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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