Standardized Test Prep

SAT/ACT

59. What is the image of P ( 11 , − 5 ) p open 11 comma negative 5 close  for the translation ( x , y ) → ( x − 12 , y − 6 ) , open x comma y close rightwards arrow open x minus 12 comma y minus 6 close comma  followed by a reflection across x = 0 ? x equals 0 question mark
    1. ( 1 , − 11 ) open 1 comma negative 11 close
    2. ( − 1 , 11 ) open negative 1 comma 11 close
    3. (1, 11)
    4. ( − 1 , − 11 ) open negative 1 comma negative 11 close

60. ABCD is a rectangular window divided into 12 panes of glass. E, F, G, and H are midpoints of A B ¯ , B C ¯ , C D ¯ , and  A D ¯ , eh b bar , comma , b c bar , comma , c d bar , comma , and . eh d bar , comma  respectively. Which statement must be true?

    

    6. The quadrilateral panes are squares.
    7. The quadrilateral panes are rhombuses.
    8. The triangular panes are all congruent.
    9. The triangular panes are right triangles.
61. A triangle has side lengths 7 in., 9 in., and x in. Which inequality must be true?
    1. 7 < x < 9 7 less than . x less than 9
    2. − 2 < x < 9 negative 2 less than . x less than 9
    3. 2 < x < 16 2 less than . x less than 16
    4. 7 < x < 16 7 less than . x less than 16
62. Δ A B C cap delta eh b c  has vertices A(0, 5), B(0, 0), and C(5, 0). Δ P Q R cap delta p q r  has vertices P(0, 15) and Q(0, 0). Δ A B C ∼ Δ P Q R . cap delta eh b c tilde operator cap delta p q r .  What are the coordinates of R?
    6. ( 0 , − 5 ) open 0 comma negative 5 close
    7. ( 0 , − 15 ) open 0 comma negative 15 close
    8. ( 15 , − 15 ) open 15 comma negative 15 close
    9. (15, 0)

Short Response

63. Δ A B C cap delta eh b c  and Δ H I G cap delta h i g  are acute triangles such that Δ A B C ≅ Δ H I G . B L ¯ cap delta eh b c approximately equal to cap delta h i g . . b l bar  and I T ¯ i t bar  are altitudes of the two triangles. Is B L ¯ ≅ I T ¯ ? b l bar , approximately equal to , i t bar , question mark  Justify your answer.

Mixed Review

Coordinate Geometry Find the image of Δ A B C cap delta eh b c  for a dilation with center (0, 0) and the given scale factor.

See Lesson 9-5.

64. A ( 0 , 4 ) , B ( 0 , 0 ) , C ( − 3 , − 1 ) ;  scale factor  3 eh open 0 comma 4 close comma b open 0 comma 0 close comma c open negative 3 comma negative 1 close semicolon . scalefactor . 3
65. A ( 4 , 2 ) , B ( 2 , 8 ) , C ( 8 , 0 ) ;  scale factor  1.5 eh open 4 comma 2 close comma b open 2 comma 8 close comma c open 8 comma 0 close semicolon . scalefactor . 1.5
66. A ( 2 , 3 ) , B ( − 4 , − 2 ) , C ( 5 , − 3 ) ;  scale factor  2 eh open 2 comma 3 close comma b open negative 4 comma negative 2 close comma c open 5 comma negative 3 close semicolon . scalefactor . 2
67. A ( 7 , 8 ) , B ( 5 , 4 ) , C ( 9 , 6 ) ;  scale factor  0.5 eh open 7 comma 8 close comma b open 5 comma 4 close comma c open 9 comma 6 close semicolon . scalefactor . 0.5

See Lesson 5-5.

Identify the two statements that contradict each other.

68. 1. Δ A B C cap delta eh b c  is a right triangle.
    2. Δ A B C cap delta eh b c  is equiangular.
    3. Δ A B C cap delta eh b c  is isosceles.
69. 1. In right Δ A B C , m ∠ B = 90 . cap delta eh b c comma m angle . b equals 90 .
    2. In right Δ A B C , m ∠ A = 80 . cap delta eh b c comma m angle . eh equals 80 .
    3. In right Δ A B C , m ∠ C = 90 . cap delta eh b c comma m angle . c equals 90 .

Get Ready! To prepare for Lesson 9-7, do Exercises 70−78.

See Review, p. 57.

Classify the polygon with the given number of sides.

70. five
71. eight
72. 12

See Lesson 6-1.

Find the measure of an angle of each regular polygon.

73. triangle
74. quadrilateral
75. hexagon
76. octagon
77. decagon
78. 14-gon

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