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Name _______________________________________________ Period ____________

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ANGLES

Solve for each variable.

1. m<AMC = 70 2. <CAT is a right angle

A C

(2x +15)

y (3y + 10) (3x)

M A

C T

3. 4.

(2x + 8)

(3x – 3) 30 (3x)

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5. The measure of A is represented by 4x and the measure of B is represented by 3x – 1. If A and

B are complementary angles, find the measure of both angles.

6. Two supplementary angles measure 5x - 30 and x + 90 degrees. What is the value of x?

7. Two vertical angles have a measure of 30° and 5x, find the value of x.

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TRIANGLES

Find the missing angles. 8. 9.

10. The measure of a base angle of an isosceles triangle is 40°. What if the measure of the vertex angle?

40° 40°

11. The measure of the vertex angle of an isosceles triangle is 20°. Find the measure of a base angle. 20°

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2 18x + 8 2x +

QUADRILATERALS

12. Given parallelogram ABCD, findm ABC .

13. Given rectangle ABCD, if AC = 4x + 16, and DB = 5x - 2, findAC .

14. Given parallelogram ABCD with 2 15D x= + , and 135B = . Find the value of x.

A

D

B

C

E

A

D C

B

A

D

B

C

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15. Given rectangle ABCD, if AE = 4x – 7 and EC = 3x + 1, find the length ofAC .

16. Polygon ABCD is a rectangle mA = 10x – 20. Find the value of x.

17. ABCD is a square. If AB = 16x – 12 and BC = 10x + 24, find the length of each side of the square.

E

A

D C

B

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REGULAR POLYGONS

18. What is the measure of one interior angle of a regular pentagon?

19. If one exterior angle of a regular polygon is 60 degrees, name the polygon.

20. What is the measure of one exterior angle of a regular octagon?

21. What is the sum of the exterior angles of a regular dodecagon?

22. What is the sum of the interior angles of a regular octagon?

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23. What is each interior angle of a 36-sided regular polygon?

24. What is the sum of the interior angles of a regular polygon with 16 sides?

25. If the measure of one exterior angle of a regular polygon is 90˚, what type of regular polygon is it?

26. What is the measure of one interior angle of a regular heptagon? Round to the nearest tenth.

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LINEAR EQUATIONS

27. Identify the slope and y-intercept of each of the following lines.

a) y = x – 3 b) – 3y = – x + 6

c) 2y = x – 4 d) y + 3 = 2x

28. State whether the given line passed through the given point.

a) x + y = 7, Point: (4, 3) b) 2y + x = 7, Point: (1, 3) c) 4x + y = 10, Point (2, -2)

29. Sketch four lines… one with a positive slope, one with a negative slope, one undefined slope and one

with a slope of zero.

Positive Negative Undefined Zero

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30. Find the slope of the line given the graph.

a) b)

31. Find the slope of a line that contains the following points.

a) (20, 8) and (9, 16) b) (9, 3) and (-6, 23)

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32. What is the slope of the line whose equation is x = 2? (Use the graph to help you.)

33. What is the slope of the line whose equation is y = -4? (Use the graph to help you.)

34. Identify the following pairs of lines as parallel, perpendicular, or neither.

a) 42

42

−=−

+−=

xy

xy b)

123

33

−=

+−=

xy

xy c)

y =3

2x

y =3

2x − 2

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35. Graph the following lines. (You may use a calculator!)

a) y = -x + 5 b) y = −1

3x + 1

36. Write an equation of a line whose slope is -2 and passes through the point (4, 2).

37. Write the equation of the line whose slope is ½ and passes through the point (-8, 1).

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38. Write the equation of a line that passes through the point (4, -6) and is parallel to the line y = -3x + 3.

39. Write the equation of a line that passes through the point (1, 5) and is perpendicular to the line

y =1

2x − 4 .

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MIDPOINT AND DISTANCE

40. Line segment AB has endpoints A(-2, 3) and B(-4, 6). What are the coordinates of the midpoint of

AB?

41. Find the midpoint of

AB given the coordinates A (5, 10) and B (3, 2).

42. M is the midpoint of . The coordinates of A are (-2, 3) and the coordinates of M are (1, 0). Find the

coordinates of B.

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43. Find the distance between the points (-5,-2) and (1,6) to the nearest tenth.

44. The coordinates of point R are (–3, 2) and the coordinates of point T are (4, 1). What is the length of

RT to the nearest 10th?

45. Find the perimeter of triangle ABC below.

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CIRCLES

46. If the radius of a circle is 8, what is the diameter?

47. If the diameter of a circle is 25, what is the radius?

48. Write the equation of a circle given the center (0, -4) and the radius 5.

49. Write the equation of a circle given the center (-3, 6) and the diameter 8.

50. Write the equation of a circle given the graph.

51. Write the equation of a circle given the graph.

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52. Write the equation of a circle given the graph.

53. Write the equation of a circle given the center (0, 0) and a point on the circle is (-3, -4).

54. Circle O has AB as a diameter. The coordinates of A are (-2, 5) and the coordinates of O, the center of the circle are (7,-1). Write the equation of circle O.

55. Find the center and radius of the circle given the equation (x + 2)2 + (y – 3)2 = 9

A

(-2, 5)

O

(7,-1)

B

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56. Find the center and radius of the circle given the equation x2 + (y + 6)2 = 5. Round to the nearest tenth.

57. Graph the circle given the equation (x – 4)2 + (y – 2)2 = 25

58. Graph the circle given the equation x2 + (y + 6)2 = 9

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PARABOLAS

59. The accompanying diagram shows the graphs of a linear equation and a quadratic equation. How many solutions are there to this system of equations? (a) 3 (b) 0

(c) 2 (d) 1

60. Identify the roots, turning point and axis of symmetry of the parabola below.

a) Roots:

b) Turning point:

c) Axis of Symmetry:

61. Identify the turning point, axis of symmetry and whether the turning point represents a maximum or minimum for the parabola below.

a) Turning point:

b) Axis of Symmetry:

c) Maximum or Minimum:

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62. Identify the roots, turning point, axis of symmetry, and whether the turning point represents a maximum or minimum of the parabola below.

a) Roots:

b) Turning point:

c) Axis of Symmetry:

d) Maximum or Minimum:

63. Identify the roots, turning point and axis of symmetry of the parabola below.

a) Roots:

b) Turning point:

c) Axis of Symmetry:

64. Find the equation for the axis of symmetry of the parabola y = x2

+ 4x +2 algebraically.

65. Find the axis of symmetry of the parabola whose equation is 382 2 +−−= xxy .

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x y

x y

66. Graph the quadratic equation y = x2

- 4x + 3.

a) Identify the roots.

b) Identify the turning point.

c) Identify the equation for the axis of symmetry.

d) Does the parabola have a maximum or minimum?

67. Graph the quadratic equation 342 −+−= xxy .

a) Identify the roots.

b) Identify the turning point.

c) Identify the equation for the axis of symmetry.

d) Does the parabola have a maximum or minimum?

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x y

x y

x y

x y

68. Given the system of equations: y = x2

+ 4x +2

y = 2x + 5

Solve the system of equations graphically.

69. Given the system of equations: y = -x

2+ x + 4

𝑦 =1

2𝑥 + 4

Solve the system of equations graphically.

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TRANSFORMATIONS

70. Which letter has both line and point symmetry?

(a) A (c) S

(b) Z (d) H

71. Which figures have both point symmetry and line symmetry?

(a) A and C, only (c) B and C, only

(b) none of the figures (d) all of the figures

72. In which figure is ΔA' B' C' a reflection of ΔABC in line l?

73. In the diagram, ΔR' S' T' is the image of ΔRST. Which type of transformation is shown in this diagram?

(a) dilation (c) reflection

(b) rotation (d) translation

74. In the diagram, which triangle is the image of Δ2 after a reflection in the x-axis?

(a) 1 (c) 2

(b) 3 (d) 4

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75. Under which transformation can the image be a different size than the original figure?

(a) translation (c) rotation

(b) dilation (d) reflection

76. The best description of a dilation of a figure is

(a) an enlargement or a reduction of the figure

(b) a slide of the figure (c) a turning of the figure about some fixed point (d) a mirror image of the figure

77. What is the total number of lines of symmetry in a rectangle?

(a) 1 (c) 2

(b) 3 (d) 4

78. Find A', the image of A(3, 5), after a reflection in the line y = x.

79. What are the coordinates of A', the image of A(2, 3) after a reflection in the x-axis?

80. What are the coordinates of the image of point (3, 4) when reflected in the y-axis?

81. What are the coordinates of the image of (4, -7) after the translation that shifts (x, y) to

(x – 6, y + 3)?

82. What is the image of (-4, -5) when reflected in the x-axis?

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83. What are the coordinates of the image of point (-1, 2) under a dilation of 3?

84. What are the coordinates of the image of (-3, 0) after a translation that shifts (x, y) to (x + 2, y - 2)?

85. What are the coordinates of A', the image of A(1, 2) after a reflection in the line y = x?

86. What is the image of (-2, 4) after a reflection in the x-axis?

87. What are the coordinates of the image of point (7, 2) after the translation (x, y) → (x − 2, y + 3)?

88. What is the image of the point (−5, 2) under the translation T3,−4?

89. What is the image of the point (2, −3) after the transformation ry-axis?

90. Which diagram shows a dotted line that is not a line of symmetry?

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91. Which letter has point symmetry but not line symmetry?

(a) H (b) S (c) T (d) X

92. As shown in the accompanying diagram, the star in position 1 on a computer screen transforms to the

star in position 2.

This transformation is best described as a (a) line reflection (b) translation (c) rotation (d) dilation

93. Which letter demonstrates line symmetry but not point symmetry?

(a) T (b) N (c) H (d) S

94. In the accompanying diagram, A B C' ' ' is the image of ABC and A B C ABC' ' ' .

Which type of transformation is shown in the diagram?

(a) line reflection (c) translation

(b) rotation (d) dilation

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95. The accompanying diagram shows the transformation of XYZ to X Y Z' ' '.

This transformation is an example of a

(a) line reflection (c) translation

(b) rotation (d) dilation

96. On the set of axes, draw and label triangle MAD with vertices M(3, 3), A(2, 4), and

D(1, 1) and apply the transformation

D3 .

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97. Triangle ABC has coordinates A(2, 0), B(1, 7), and C(5, 1). On the accompanying set of axes,

graph, label, and state the coordinates of ABC and ,''' CBA the reflection of ABC in the x-axis.