Pre-Calculus Homework Solutions 132

Pre-Calculus Homework Solutions 132 - 23. Given: a 0, b 0,...

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23. Given: a . 0, b . 0, and a . b Prove: } a b } . 1 Proof: Step 1 Assume that } a b } ± 1. Step 2 Case 1 Case 2 } a b } ¬ , ¬ 1 } a b } ¬ 5 1 a ¬ , ¬ ba ¬ 5 b Step 3 The conclusion of both cases contradicts the given fact a . b . Thus, } a b } . 1. 24. Given: A w B w > @ A w C w Prove: / 1 > @ / 2 Proof: Step 1 Assume that / 1 > / 2. Step 2 If / 1 > / 2, then the sides opposite the angles are congruent. Thus A w B w > A w C w . Step 3 The conclusion contradicts the given information. Thus / 1 > / 2 is false. Therefore, / 1 > @ / 2. 25. Given: n ABC and n ABD are equilateral. n ACD is not equilateral. Prove: n BCD is not equilateral. Proof: Step 1 Assume that n BCD is an equilateral triangle. Step 2 If n BCD is an equilateral triangle, then B w C w > C w D w > D w B w .Since n ABC and n ABD are equilateral triangles, A w C w > A w B w > B w C w and A w D w > A w B w > D w B w .By the Transitive Property, A w C w > A w D w > C w D w . Therefore, n ACD is an equilateral triangle. Step 3 This conclusion contradicts the given information. Thus, the assumption is false.
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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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