Pre-Calculus Homework Solutions 144

# Pre-Calculus Homework Solutions 144 - 22 Given PR PQ SQ...

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22. Given: PR PQ , SQ SR Prove: m 1 m 2 Proof: 23. Given: ED DF ; m 1 m 2; D is the midpoint of CB ; AE AF . Prove: AC AB Proof: 24. Given: RS ¬ UW ST ¬ WV RT ¬ UV Prove: m S m W Indirect Proof: Step 1 Assume m S m W . Step 2 If m S m W , then either m S m W or m S m W . Case 1: If m S m W , then RT UV by the SAS Inequality. Case 2: If m S m W , then RST UWV by SAS, and RT UV by CPCTC. Thus RT UV . Step 3 Both cases contradict the given RT UV . Therefore, the assumption must be false, and the conclusion, m S m W , must be true. 25. As the door is opened wider, the angle formed increases and the distance from the end of the door to the door frame increases. 26. By the SAS Inequality Theorem, if the tree started to lean, one of the angles of the triangle formed by the tree, the ground, and the stake would change, and the side opposite that angle would change as well. However, with the stake in the ground and fixed to the tree, none of the sides of the triangle can change length. Thus, none of the angles can change. This ensures that the tree will stay straight.
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