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Pre-Calculus Homework Solutions 253

Pre-Calculus Homework Solutions 253 - 41 Given AB DC AB DC...

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255 Chapter 8 For (2, 2) and (0, 4), RT QS . slope of SR ¬ 1 1 ( ( 1 1 ) ) ¬ 1 Suppose T is (0, 4). slope of QT ¬ 0 4 ( 2 2) ¬ 1 So SR QT . So, (2, 2), ( 4, 0), and (0, 4) are the possibilities for the fourth vertex. Any of these values results in both pairs of opposite sides being parallel, and thus, the four points form a parallelogram. 37. JKLM is a parallelogram because KM and JL are diagonals that bisect each other. 38. If both pairs of opposite sides are parallel and congruent, then the watchbox is a parallelogram. 39. Given: AD BC AB DC Prove: ABCD is a parallelogram. Proof: 40. Given: AE EC , DE EB Prove: ABCD is a parallelogram. Proof: 41. Given: AB DC AB DC Prove: ABCD is a parallelogram. Proof: 42. This theorem is not true. ABCD is a parallelogram with diagonal BD , ABD CBD . 43. Given: ABCDEF is a regular hexagon. Prove: FDCA is a parallelogram. Proof: 44. Sample answer: The roofs of some covered bridges are parallelograms. The opposite sides are congruent and parallel. Answers should include the following.
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