GEOMETRY EXAM REVIEW
NAME _______________________________
In algebra, there are functions. For example,
1. What is the value of the function,
A) 50
B) 0
2. What is the value of the function,
A)
2
7
f ( x)  x 2  5 x when x = -5?
C) 15
D) 25
f (x) = 7x + 3 when x = 5?
B) 15
C) 28
D) 38
In geometry, this is called a mapping. Mappings are represented as coordinate rules. For example,
3. Given coordinate rule,
T (x, y) - - - - >(2x, y + 7) determine the image of A(-2,2)?
4. Given coordinate rule,
T (x, y) - - - - >(x - 4,5y) determine the pre-image of A’ (-6,15)?
5. In algebra if a function has the same number of input vales as output values this is called a one to one function. In geometry,
this is called a transformation where there are the same number of pre-image points and image points. List the 5 common
transformations.
____________________
____________________
____________________
____________________
____________________
6. An isometric transformation (or rigid motion) preserves the shape through the transformation (i.e. it stays congruent). List the
3 isometric transformations.
____________________
____________________
Using the above image, answer the following questions.
7. Does the shape have line symmetry?
YES
NO
8. If yes, how many lines of symmetry does it have? _________
9. Does the shape have rotational symmetry?
YES
NO
10. If yes, what is the order of rotation? _________
Angle of rotation? __________
11. Does the shape have point symmetry?
YES
NO
____________________
12. Write the rule for each reflection.
R x axis (x , y) = ( ______ , _______ )
R y axis (x , y) = ( ______ , _______ )
R y = x (x , y) = ( ______ , _______ )
13.
R x axis (-3 , 8) = ( ______ , _______ )
14.
R x axis ( ______ , _______ ) = (5, -1)
15.
R y axis (3, -7) = ( ______ , _______ )
16.
R y axis (______ , _______) = (-6, 4)
15.
R y=x (10, 0) = ( ______ , _______ )
16.
R y=x (______ , _______) = (1, -2)
17. Write the rule for each rotation.
R O, 90o (x , y) = ( ______ , _______ )
R O, 180o (x , y) = ( ______ , _______ )
R O, 270o (x , y) = ( ______ , _______ )
18.
R O, 90o (-3 , 8) = ( ______ , _______ )
19.
R O, 90o ( ______ , _______ ) = (5, -1)
20.
R O, 180o (3, -7) = ( ______ , _______ )
21.
R O, 180o (______ , _______) = (-6, 4)
22.
R O, 270o (10, 0) = ( ______ , _______ )
23.
R O, 270o (______ , _______) = (1, -2)
Given the translation rule, find the missing point.
24.
T (x,y) ------> (x – 2, y + 7)
A ( 3 , -2)
A’ ( ______ , ______ )
25.
T (x,y) ------> (x , y + 3)
A ( ______ , ______ )
A’ (- 5, 8)
Are the following pairs of triangle congruent? If YES, name the congruence postulate (SSS, SAS, ASA, AAS, or HL). If
NO, write none.
26. ______________
27. ________________
28. __________________
29. _________________
B
C
J
o
* *
C
A
D
A
16
13
2
1
3
15
14
4
12
5
6
7
8
9
11
10
Use the figure above to name each angle pair relationship.
30. 1 & 6
_________________________
31. 16 & 14 _________________________
32. 1 & 7
_________________________
33. 12 & 14 _________________________
o P
Use the figure on the previous page to find each measurement.
34. If m1 = 127°, then the m3 = ____________
35. If m10 = 107°, then the m16 = ___________
36. If m4 = 62°, then the m5 = ____________
37. If m15 = 49°, then the m11 = ____________
2
2
3
1
3
1
4
4
38. If m1 = 14x + 12
and m3 = 20x – 6,
find x.
39. If m2 =10x+3and
the m3 = 17x-12, find
m2.
40. If m3 = x + 19, the
m6 = 10x + 7, find
m6.
41. If m8 = 20x - 8,
and the m4= 16x+
16, find x.
______________
______________
______________
_____________
Cirlce True or False.
42. In a parallelogram, the diagonals are congruent.
T
F
43. Diagonals are angle bisectors in a square.
T
F
44. All squares are rhombi.
T
F
45. In a rectangle, the diagonals are perpendicular.
T
F
T
F
46. Consecutive angles are supplementary in a square.
B
A
47. ABCD is a parallelogram.
E
C
D
ADC = 81. Find DCB.
__________________
A
48.. ABCD is a rectangle.
B
E
C
D
̅̅̅̅ = 1𝑥 + 10 and 𝐸𝐶
̅̅̅̅ = 3𝑥 + 2. Find 𝐷𝐵.
̅̅̅̅̅
𝐴𝐸
_________________
For each given scale factor, determine if the dilation is a reduction or enlargement.
49.
2:1
___________
50.
3
4
___________
51.
.35
___________
52.
4
___________
53..
8
7
___________
Find the RATIO for each using the given triangle.
54) sin A = ____________
55) tan C = _____________
56) cos A = _____________
58.
59.
Solve for x ( or 𝚯).
57.
x
x
28°
62°
7 cm
21 cm
24 cm
60. The angle of depression from the helicopter to the girl is:
A) 1
B) 2
C) 3
D) 4
61. The angle of elevation from the island to the airplane is:
A) 1
B) 2
C) 3
D) 4
B
E
A
C
D
62. Which of the following is NOT a chord?
A. AB
B.
AC
DC
C. AE
D.
C. 4
D. 5
C. AE
D.
63. How many radii are in the diagram?
A. 2
B. 3
64. Which of the following is a diameter?
A. AB
B.
AC
DC
15 cm
θ
A
F
B
E
D
C
65. Which of the following is a secant?
A.
B.
AC
C.
DC
D.
C.
DC
D.
66. Which of the following is a tangent?
A.
B.
67. Which of the following is the point of tangency?
A.
E
B.
D
C.
C
D.
A
68-69. Find the center (#68) and radius (#69) of the given circle.
 x  1
2
68.Center
  y  2   16
(_____ , _____)
2
69. Radius = _______
70. Determine the equation of circle C.
70. __________________________
Radius = 4 cm C (-8,5)
71. What is the equation of the circle on the graph?
A.
x2   y  2  9
B.
C.
x2   y  2  9
 x  2
D.
2
2
72. Determine the standard equation of the circle.
x 2  y 2  18x  20 y  12  0
73. Find x.
D
C
77 cm
B
5x - 3
A
 x  2
2
2
 y2  3
 y2  9
72. __________________________
74. Is
tangent to circle C?
B
75-76. Find x and y
15 cm
C
20 cm
25 cm
A
77. Find x.
78. Find x.
79. Find x.
80. Complete the two-column proof.
Given: 4x – 8 = 7x + 4
STATEMENTS
Prove: x = -4
REASONS
81. Complete the two-column proof.
Find the area.
82.
83.
84.
86.
87.
Find the volume.
85.