Name: _________________________
Period: _____
STUDY GUIDE FOR THE FINAL EXAM
CHAPTER 1
Use the diagram to answer the following questions #1-3.
N
1. Give two other names for
A
.
W
2. Give two other names for plane
S
.
P
3. Name three points that are collinear. Name four points that are coplanar.
F
a
O D
d
4. Classify the polygon by the number of sides. Tell whether it is convex or concave.
5. Write three names for the angle.
T
L
Y
In the figure,
,
,
, and
.
Z
P
6. Name a pair of complementary angles.
Q
R
7. Name a pair of supplementary angles.
S
O
8. Name a pair of adjacent angles.
D
T
9.Point M is the midpoint of
4x + 13
A
10.
. Find BM.
3x + 17
M
B
You are making a picture frame in shop class. Two pieces of wood are cut to form complementary
angles so they fit together properly. One angle needs to be
and the other angle needs to be
. What is the measure of the larger angle?
11.Two angles form a linear pair. The measure of one angle is eight times the measure of the other angle. Find
the measure of the larger angle.
12.The measure of an angle is nine times the measure of its complement. Find the measure of the larger angle.
13.Point B is between points A and D, and point C is between points B and D. Which are possible lengths of
when
,
, and
?
14. The midpoint of
is
. One endpoint is
15. Find the area of the polygon with vertices
,
16. Find the perimeter of the polygon with vertices
17. In the diagram,
. Find
. Find the coordinates of endpoint G.
,
,
, and
,
.
, and
.
.
18. The midpoint of segment JK is M(6, 3).
One endpoint is J (14,9).
Find the coordinates of endpoint K.
C
B
(9x + 46)°
Chapter 2
19.
(7x + 34)° D
A
Find the values of x and y.
(5y + 68)°
(3x + 18)°
(5x + 2)°
(3y + 96)°
20.
In the diagram,
3
4
2
5
1
and
. Which angle measures are possible?
In the diagram, AB = CD, BC = 3, AC =
, and BD =
. Match the numbered equation
or reason below with its corresponding letter (a - g) to show that AB = .
E
A
B
3
C
D
Equation
1.
,
Reason
,
1. Given
,
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
a.
b.
c.
d. Segment Addition Postulate
2.
3.
4. Segment Addition Postulate
5.
6.
7. Addition
8. Addition
9.
10.
11. Simplify
12.
e.
f.
g.
____ 21. Equation 2
____ 22. Reason 3
____ 23. Reason 5
____ 24. Equation 6
____ 25. Reason 9
____ 26. Equation 10
____ 27. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the conditional
statement. Then decide whether it is true or false.
____ 28. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the converse. Then
decide whether it is true or false.
____ 29. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the inverse. Then
decide whether it is true or false.
____ 30. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the contrapositive.
Then decide whether it is true or false.
____ 31. If
and
, then
.
a. Transitive Property of Angle Congruence
b. Symmetric Property of Angle Congruence
c. Reflexive Property of Angle Congruence
State the postulate illustrated by the diagram.
____ 32.
a. Plane Intersection Postulate
b. Plane-Line Postulate
c. Two Point Postulate
d. Line-Point Postulate
a. Two-Point Postulate
b. Plane-Point Postulate
c. Three Point Postulate
d. Plane Intersection Postulate
a. Two Point Postulate
b. Line Intersection Postulate
c. Three Point Postulate
d. Line-Point Postulate
a. Plane Intersection Postulate
b. Plane-Line Postulate
c. Plane-Point Postulate
d. Line Intersection Postulate
a. Two Point Postulate
b. Plane-Line Postulate
c. Line-Point Postulate
d. Line Intersection Postulate
____ 33.
____ 34.
____ 35.
____ 36.
Identify the numbered statement or reason in the two-column proof.
Given
Prove
STATEMENTS
1.
REASONS
1. Given
2.
3.
2.
3.
4.
5.
6.
4. Transitive Property of Equality
5.
6. Subtraction Property of Equality
____ 37. What is Reason 2?
a. Subtraction Property of Equality
b. Transitive Property of Equality
c. Reflexive Property of Equality
d. Symmetric Property of Equality
____ 38. What is Reason 3?
a. Definition of complementary angles
b. Substitution Property of Equality
c. Angle Addition Postulate
d. Linear Pair Postulate
____ 39. What is Statement 4?
a.
b.
c.
d.
____ 40. What is Reason 5?
a. Addition Property of Equality
b. Angle Addition Postulate
c. Multiplication Property of Equality
d. Substitution Property of Equality
CHAPTER 3
41. In the diagram,
. Find the value of y.
74°
b
c
(2 y + 34)°
42. Find the value of x that makes
a
.
b
(2x + 25)°
55°
c
d
43. Write an equation of the line passing through the point
that is parallel to the line
44. Write an equation of the line passing through the point (9, 3) that is perpendicular to the line
.
In the diagram, think of each segment in the figure as part of a line.
45. Name the line(s) through point D that appear parallel to
a.
c.
b.
and
d.
46. Name the line(s) through point B that appear skew to
a.
c.
b.
.
and
d.
.
and
47. Name the line through point D that appears perpendicular to
a.
c.
b.
48. Classify the pair of numbered angles.
d.
.
.
49. Classify the pair of numbered angles.
50. Classify the pair of numbered angles.
List all:
51. Corresponding angles:
52. Alternate Interior angles:
53. Alternate Exterior angles:
54. Consecutive Interior angles:
55. Find the value of x.
56. Find the value of x that makes line s parallel to line t.
57. Find the distance from point P to QS .
58. Write an equation of the line passing through point P1,  4 that is parallel
to y   6 x  8.
59. Write an equation of the line passing through point P 1, 3 that is
perpendicular to y  4 x  7.
CHAPTER 4
60.
Graph
with endpoints C(–8, 2) and D(–5, 6) and its image after the composition.
Translation:
Translation:
61. The logo for a business is moved across a page 6 units right and 6 units down. Next, it is moved 2 units
left and 2 units up. Rewrite the composition as a single translation.
62. Graph
with points F(–3, –4) and G(–3, –2)
and its image after the reflection in the line
.
63. Describe the similarity transformation that maps
to
(dilations have a center at the
origin).
y
12
B
8
a. rotation 180° about the origin followed by a dilation with a
scale factor of
b. rotation 90° counterclockwise about the origin followed by a
A
4
T
–12
–8
dilation with a scale factor of
R
–4
4
8
12
x
c. rotation 180° about the origin followed by a dilation with a
–4
S
scale factor of
–8
d. rotation 90° counterclockwise about the origin followed by a
dilation with a scale factor of
C
–12
64. You are rotating a figure 152° from G to
intersecting lines so that G can be mapped to
. Find the measure of the acute angle formed by
using two reflections.
65. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.
P
P'
12
a. 30; enlargement
c. 30; reduction
b. 2
; reduction
7
d. 7
; enlargement
2
C
CP = 42
66. Graph
with endpoints at
and
and its image after the composition.
Translation:
Rotation: 90° counterclockwise about the origin
67. In the diagram,
,
is reflected in line k,
is reflected in line j,
centimeters, and the
distance from to line j is 12 centimeters. Which of the following statements are true?
k
A
j
a. The distance from A to line k is 3
centimeters.
b.
cm
c.
line j
d. A rotation maps
onto
.
A'
B
A''
B'
B''
68. Graph
with endpoints at
and
and its image after the composition.
Rotation: 180° about the origin
Reflection: in the line
69. How many lines of symmetry does the rhombus have?
Chapter 5
70.
A ramp is designed with the profile of a right triangle. The measure of one acute angle is 2 times the
measure of the other acute angle. Find the measure of each acute angle.
71.
Find
.
40°
28°
72.
Find the value of x.
A
x
60°
C
60°
13
B
Can the triangles be proven congruent with the information given in the diagram? If so, state the
theorem you would use.
73.
74.
75. Which reason is not necessary to explain how you can find the distance across the lake?
a.
b.
c.
d.
e.
ASA Congruence Theorem
Right Angles Congruence Theorem
SSS Congruence Theorem
Corresponding parts of congruent triangles are congruent.
Vertical Angles Congruence Theorem
76. Which reason is not used in a plan to prove that
a. ASA Congruence Theorem
b. Reflexive Property of Congruence
77.
?
c. SSS Congruence Theorem
d. Congruent Complements Theorem
Which reason is not used in a plan to prove that
a. HL Congruence Theorem
b. Reflexive Property of Congruence
?
c. Base Angles Theorem
d. Corresponding parts of congruent triangles
are congruent.
78.
Which reason is not used in a plan to prove that
?
a. Corresponding parts of congruent triangles c. Congruent Complements Theorem
are congruent.
b. Reflexive Property of Congruence
d. Alternate Interior Angles Theorem
79.
In the diagram,
that are congruent.
passes through the center C of the circle and
a.
b.
c.
d. not enough information
Match the numbered statement below with its reason to prove that
a.
b.
c.
d.
____ 80. 1.
____ 81. 2.
____ 82. 3.
____ 83. 4.
. Name two triangles
Third Angles Theorem
Given
All corresponding parts are congruent.
Reflexive Property of Congruence
.
____ 84. 5.
____ 85. 6.
____ 86. 7.
CHAPTER 6
In Exercises 87-90, find the indicated measure. Explain your reasoning.
87. AD
88. GJ
90. mDGF
89. PQ
In Exercise 91, find the coordinates of the circumcenter of the triangle with the
given vertices.
91.
J 6, 0, K 0, 0, L0, 4
In Exercise 92, P is the incenter of triangle QRS. Use the given information to
find the indicated measure.
92. PJ  4x  8, PL  x  7
Find PK .
In Exercises 93-94, point P is the centroid of triangle ABC. Use the given
information to find the indicated measures.
94. CP  16
93. BL  12
Find BP and PL.
Find PL and CL.
In Exercise 95, find the coordinates of the centroid of the triangle with the given
vertices.
95.
Q2, 6, R4, 0, S 10, 6
In Exercises 96-100, use the graph of triangle ABC.
96. In triangle ABC. show that the midsegment ED
is parallel to BC and that ED  1 BC.
2
97.Find the coordinates of the endpoints of
midsegment EF , which is opposite AC .
98. Show that EF is parallel to AC and that EF  1 AC.
2
99. State the coordinates of the endpoints of midsegment DF .
100. Show that DF is parallel to AB and DF  1 AB.
2
In Exercises 1 0 1- 1 0 3, use triangle QRS, where A, B, and C are the midpoints of
the sides.
101. When AB  16, what is QS?
102. When CA  3x  1 and SR  5x  4, what is CA?
103. When QR  5x  2 and CB  2 x  5, what is AR?
In Exercises 104-105, list the angles of the given triangle from smallest to
largest.
104.
105.
In Exercises 106-107, list the sides of the given triangle from shortest to longest.
106.
107.
In Exercises 108-109, is it possible to construct a triangle with the given side
lengths? Explain.
108. 15, 37, 53
109. 9, 16, 8
In Exercises 110-113, copy and complete the statement with , , or  . Explain your reasoning.
110. AC _____ DF
111. mHGI _____ mIGJ
112. m1 _____ m2
113. KL _____ MN