For a trapezoid, consider the segment joining the midpoints of the two given segments. How are its length and the lengths of the two parallel sides of the trapezoid related? Justify your answer.

64. the two nonparallel sides
65. the diagonals

66. B N ↔ modified b n with left right arrow above is the perpendicular bisector of A C ¯ eh c bar at N. Describe the set of points, D, for which ABCD is a kite.

    

Standardized Test Prep

SAT/ACT

67. Which statement is never true?
    1. Square ABCD is a rhombus.
    2. Trapezoid GHJK is a parallelogram.
    3. Parallelogram PQRS is a square.
    4. Square WXYZ is a parallelogram.
68. A quadrilateral has four congruent sides. Which name best describes the figure?
    6. trapezoid
    7. parallelogram
    8. rhombus
    9. kite

69. How would you classify triangle LMN?

    

    1. acute isosceles
    2. right isosceles
    3. obtuse scalene
    4. acute scalene

Extended Response

70. Given D E ¯ d e bar is congruent to F G ¯ f g bar and E F ¯ e f bar is congruent to G D ¯ , g d bar , comma prove ∠ E ≅ ∠ G . angle , e approximately equal to , angle g .

Mixed Review

See Lesson 6-5.

Find the value of x for which the figure is the given special parallelogram.

71. 

    Rhombus

72. 

    Rectangle

73. 

    Rhombus

See Lesson 6-1.

74. Algebra Find the value of c.

    

Get Ready! To prepare for Lesson 6-7, do Exercises 75 and 76.

See Lesson 1-7.

75. Given A(6, − 2 negative 2 ) and B ( − 4 , b open negative 4 comma 8), find the midpoint and the length of A B ¯ . eh b bar , .

See Lesson 3-7.

76. Find the slope of the line containing the points C( − 1 , negative 1 comma 5) and D(7, 3).

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