41. Developing Proof Complete the flow proof of Theorem 6-15.

    Given: ABCD is a rectangle.

    Prove: A C ¯ ≅ B D ¯ eh c bar , approximately equal to , b d bar

    

    
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Algebra Find the value(s) of the variable(s) for each parallelogram.

42. R Z = 2 x + 5 , r z equals , 2 x plus 5 , comma
    S W = 5 x − 20 s w equals . 5 x minus 20

    

43. m ∠ 1 = 3 y − 6 m angle , 1 equals . 3 y minus 6

    
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44. B D = 4 x − y + 1 b d equals , 4 x minus . y plus 1

    

45. Proof Prove Theorem 6-14.

    Given: ABCD is a rhombus.

    Prove: A C ¯ eh c bar bisects ∠ B A D angle b eh d and ∠ B C D . angle b c d .

    

46. Writing Summarize the properties of squares that follow from a square being (a) a parallelogram, (b) a rhombus, and (c) a rectangle.

47. Algebra Find the angle measures and the side lengths of the rhombus below.

    

48. Open-Ended On graph paper, draw a parallelogram that is neither a rectangle nor a rhombus.

Algebra ABCD is a rectangle. Find the length of each diagonal.

49. A C = 2 ( x − 3 ) eh c equals . 2 open x minus 3 . close and B D = x + 5 b d equals , x plus 5
50. A C = 2 ( 5 a + 1 ) eh c equals . 2 open 5 eh plus 1 . close and B D = 2 ( a + 1 ) b d equals . 2 open eh plus 1 . close
51. A C = 3 y 5 eh c equals , fraction 3 y , over 5 end fraction and B D = 3 y − 4 b d equals , 3 y minus 4
52. A C = 3 c 9 eh c equals , fraction 3 c , over 9 end fraction and B D = 4 − c b d equals , 4 minus , c

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