2
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)
3
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.
4
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°
5
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
6
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
7
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?
8
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.
9
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
10
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)
11
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
12
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).
13
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 .
14
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.
15
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.
16
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
19
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:
20
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 .
21
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?
22
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.
23
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?
25
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?
26
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
27
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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