Honors Geometry
Semester 1 Exam Review
Show all your work whenever possible.
1.
Describe what the notation RS stands for.
Illustrate with a sketch.
2.
What do P Q and Q P have in common?
3.
Draw four points, A, B, C, and D, on a line so that
C B and C A are opposite rays and C D and C A
are the same ray.
4.
Draw two planes that intersect at JK . Draw P Q so that
it intersects JK at point J. Are JQ and JK coplanar?
Explain your answer.
5.
If RS = 44 and QS = 68, find QR.
6.
R, S, and T are collinear. S is between R and T. RS = 2w + 1,
ST = w – 1, and RT = 18. Use the Segment Addition Postulate
to solve for w. Then determine the length of RS
7.
Find AB and BC in the situation shown.
AB = x + 16, BC = 5x + 10, AC = 56
Name:
Hour:
__
8.
Find the distance between the points (1, 4) and (–2, –1).
9.
The distance between points A and B is _______.
10.
Find the midpoint of the segment with
endpoints (9, 8) and (3, 5).
11.
Find the circumference of the circle. Use  = 3.14.
12.
Find the area. All lengths are in centimeters.
9.7
6.5
7.2
2.4
13.
A wooden fence is to be built around a 50 m-by-62 m lot.
How many meters of fencing will be needed? If the wood
for the fence costs $47.75 per meter, what will the wood
for the fence cost?
14.
In the figure (not drawn to scale), M O bisects LMN
mLMO = (15x  21)° and mNMO = (x + 63)°.
Solve for x and find m LMN.
15.
mOMN = (2x +9)° and mLMN = (6x  7)°)° and mOML = 66°.
Find mOMN and mLMN.
16.
The first three members of a sequence are shown. How many dots are in the fourth member of the sequence?
17.
If the pattern were continued, what would be the ratio of the number of unshaded squares to the number of shaded squares in the next
figure in the pattern?
18.
If PQ = 3 and PQ + RS = 5, then 3 + RS = 5 is an example of the __________.
a.
b.
c.
d.
Substitution Property of Equality
Multiplication Property of Equality
Transitive Property of Equality
Reflexive Property of Equality
19.
Name the property which justifies the following conclusion:
Given: b + c  d = e and d = a
Conclusion: b + c  a = e
20.
Name the property which justifies the following conclusion:
Given: 18x = 288
Conclusion: x = 16
In 21 and 22, identify the property that makes the statement true.
21.
If XY = MN, then MN = XY.
22.
If mP = mR and mR = mT, then mP = mT.
23.
1 and 2 form a linear pair. If m2 = 67°, what is m1?
24.
Write a two-column proof.
Given: AOC and COB are a linear pair
Prove: AOC and COB are supplementary
C
A
B
O
25.
Write a two-column proof.
Given: AOC and COB are a linear pair
Prove: mAOC + mCOB = 180°
C
A
B
O
26.
Provide the reasons for statements 3 and 5 in the proof.
Given: 1 and 2 form a linear pair; m2 = 100°
Prove: m1 = 80°
27.
Provide reasons for each statement in the proof.
Given: 3  4
Prove: 1  2
28.
1 is complementary to 2; 3 is complementary to 2.
What theorem, property, or postulate allows you to state
that 1  3?
29.
Complete the proof.
Given: 2  4
Prove: 1 3
Write a two-column proof.
30.
Given: 1 and 2 are vertical angles; 1 and 3 form a linear pair
Prove: 2 and 3 are supplementary angles
31.
Given: BE bisects AGC
Prove: BGC  DGE
32.
In the figure, l // n and r is a transversal. Which of the following is not necessarily true?
a.
b.
33.
8  2
2  6
c.
d.
5  3
7  4
A dirt path connects the lanes of a divided highway that runs east-west.
An officer in a police car headed east gets a call that requires crossing
over to the westbound lanes using the dirt path. Through what angle
must the police car turn at the bend in the dirt path?
Westbound
Lanes
46°
38°
Eastbound
Lanes
34.
Given that a // b, what is the value of x? (The figure may not be drawn to scale.)
35.
Which lines, if any, can be proved parallel given the following diagram? For each conclusion, provide the justification.
a
b
c
d
29°
151°
36.
Find the slope of the line passing through
the given points
a. A(6, –5) and B(–5, –7)
b. A (-2,-3) and B (5,3)
37.
Consider the line graphed at the right (scaled by 1). In standard form, write the equation of the line
a.
perpendicular to this line through the point (4, 3)
b.
parallel to this line through the point (5, 3)
•
•
38.
Which best describes the relationship between the line that passes through
(7, 1) and (10, 5) and the line that passes through (–8, 5) and (–5, 9)?
a.
b.
c.
d.
39.
same line
perpendicular
neither perpendicular nor parallel
parallel
Find the slope of a line perpendicular to the line containing the points (3, –7) and (4, –3).
40.
Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither.
Line 1 passes through (4, –6) and (6, –2)
Line 2 passes through (7, –8) and (11, –6)
41.
Tell whether the lines through the given points are parallel, perpendicular, or neither. Explain.
Line 1: (2, 2), (4, 5)
Line 2: (4, 9), (6, 4)
42.
Find the slope-intercept form of the line passing through the
point (9, 8) and parallel to the line y = 8x + 5
43.
Identify the x- and y-intercepts of the graph of the equation 6x  4y = 2?
44.
Graph the linear equation 8x  2y = 12 by finding x- and y-intercepts.
45.
Find the measure of the interior angles to the nearest tenth. (Drawing is not to scale.)
(2x + 2)°
(x + 1)°
(2x + 1)°
46.
Refer to the figure below. Find mA.
A
106°
39°
47.
Find x.
48.
Solve for x, given that A B  BC . Is ABC equilateral?
A
7
x3
B
x1
C
49.
Refer to the figure shown. Which of the following statements is true?
a.
b.
50.
c.
d.
State two postulates or theorems that can be used to conclude that AOB  COD.
D
A
O
C
B
51.
Find the length of LM . State the postulate or theorem you use.
M
N
L
350
P
350
290
O
52.
Line l is the perpendicular bisector of M N . Find the value of x.
l
M
N
10x  21
8x + 3
53.
Given: BAC  DAC, DCA  BCA
Prove: BC  DC
.
54.
Given: BAC  DAC, B  D
Prove: BC  DC
55.
Given: P R and Q S bisect each other
Prove: PQR RSP
56.
Given mWXY = mWYX; WX = 3n + 5, WY = 6n  3; XY = 9; find WX
Y
X
W
Use the diagram for Exercises 57 and 58.
57. _______
58. _______
59. _______
60. _________ Name the vector and write its component form.
61. _______ What is the component form of the vector that describes
the translation of a point P(6, -3) to P  (-2, 4)?
A.
8,7
B.
 8,7
C.
8,7
D.
 8,7
62. a. Translate the triangle 4 units up and 2 units left. Graph and label image.
b. Find the coordinates of the vertices P  , Q  and R  after the translation.
____________
___________
___________
c. Write the components form of the vector that describes the translation.
63. _______ What are coordinates of the image of the point (4, 5) when it is reflected over the
line y = 2?
A. (2, 5)
B. (4, 3)
C. (0, 5)
D. (4, -1)
64. _______ The point J(4, 3) is reflected over the line x = 3. It is reflected again over the line
x = -1. What are the coordinates of the resulting point?
A. (-2, 3)
B. (2, 3)
65. The endpoints of AB are A (2, 1) and B(3, -1).
Graph the line segment and then reflect the
segment over the line y = -x.
C. (-4, 3)
D. (0, 3)
66.
67. _____ A dilation with its center at the origin maps A (9, -12) to
factor?
A. k =
4
3
B. k =
5
4
C. k =
A (15, -20).
5
3
What is the scale
D. k =6
68. The vertices of LMN are L(1, 3), M(3, 2), and N(2, 4).
Graph LMN and its image after the glide reflection.
Translation (x, y)  (x + 1, y – 6)
Reflection: in the y-axis
69. _______ The endpoints of
PQ
are P(3, -1) and Q(4, -2). What are the coordinates of the endpoints

after a rotation of 90 about the origin, followed by a reflection in the line y = x?
A.
C.
P  (-3, 1), Q  (-4, 2)
P  (3, 1), Q  (4, 2)
B.
P  (-1, 3), Q  (-2, 4)
D. P  (-1, -3), Q  (-2, -4)
70. _______The vertices of ABC are A(1, 6), B(6, 4) and C(3, 7). Find the coordinates of the vertices
_______ after a composition of the transformations listed.
_______ Translation : (x, y)  (x – 2, y + 3)

Rotation: 180 about the origin.
Reflection: in the x-axis.
71. _______ How many lines of symmetry does a regular hexagon have?
A. 1
B. 2
C. 3
D. 6
72. _______ How many lines of symmetry does the object at right have?
A. 2
B. 4
C. 6
D. 8
73. Describe the line symmetry and rotational symmetry of a regular nonagon.
_____________________________________________________________________________________
74. _______Identify the line symmetry and rotational symmetry of the figure at the right.
A. 6 lines of symmetry, 60
B. 3 lines of symmetry, 60


rotational symmetry
rotational symmetry

C. 6 lines of symmetry, 120 rotational symmetry

D. 3 lines of symmetry, 120 rotational symmetry
75.
Solve for x given BD = 3x + 3 and AE = 4x + 8. Assume B is the midpoint of A C and D is the midpoint of C E
C
B
D
A
E
76.
Mr. Jones has taken a survey of college students and found that 60 out of 64 students are liberal arts majors. If a college has 7723 students,
what is the best estimate of the number of students who are liberal arts majors?
77.
A worker in an assembly line takes 5 hours to produce 26 parts. At that rate, how many parts can she produce in 20 hours?
78.
Solve the proportion
79.
While visiting a daycare center, you estimate the ratio of toddlers to infants as
many of them are infants?
80.
A triangle with a perimeter of 63 feet has side lengths in the extended ratio of 6 : 7 : 8. Find the side lengths of the triangle.
81.
Use the figure to find mCED. The figure is not drawn to scale.
5
x 1

7
x
.
If the center has an enrollment of 30 children, about how
82.
Late in the afternoon, a man who is 6 feet tall casts a 15-foot shadow. He is not far from a tower 68 feet tall. How long, in feet, is the shadow
of the tower?
.
83.
One way to show that two triangles are similar is to show that ______.
a. two angles of one are congruent to two angles of the other
b. two sides of one are proportional to two sides of the other
c. a side of one is congruent to a side of the other
d. an angle of one is congruent to an angle of the other
84.
Shown below is an illustration of the ______.
85.
The postulate or theorem that can be used to prove that the two triangles are similar is _____.
86.
In
and
so, write a similarity statement.
87.
Find the value of x to one decimal place.
88.
For the figure shown, which statement is not true?
a.
b.
In
and
c.
State whether the triangles are similar, and if
d.
89.
Given: PQ // BC . Find the length of
.
y
x
90. The dashed triangle is the image of the solid triangle formed by a dilation
centered at the origin. What is the scale factor?
91.
The dotted triangle is the image of the solid triangle. What is the scale factor?
Honors Geometry Semester 1 Review
Answer Section
1.
ANS:
A ray from R through S
DIF:
2.
Level A
BLM:
Comprehension
BLM:
Application
BLM:
Application
ANS:
All of the points on
DIF:
3.
ANS:
Answers may vary.
DIF:
4.
Level B
Level B
ANS:
Yes. Since any 3 points not on the same line lie in exactly one plane, points J, Q, and K are coplanar. Since the plane containing these
three points also contains both
DIF:
5.
Level C
BLM:
Analysis
Level B
BLM:
Application
Level B
BLM:
Application
ANS:
13
DIF:
7.
,
ANS:
24
DIF:
6.
and
ANS:
AB = 21, BC = 35
and
must be coplanar.
DIF:
8.
Level B
BLM:
Application
Level A
BLM:
Application
Level B
BLM:
Application
Level A
BLM:
Application
Level B
BLM:
Application
Level B
BLM:
Application
Level B
BLM:
Application
Level B
BLM:
Application
ANS:
34
DIF:
9.
ANS:
DIF:
10.
ANS:
(6,
13
)
2
DIF:
11.
ANS:
69.08 in.
DIF:
12.
ANS:
DIF:
13.
ANS:
224 m, $10,696.00
DIF:
14.
ANS:
6, 138°
DIF:
15.
ANS:
m OMN = 25° and m LMN = 41°
DIF:
16.
Level C
BLM:
Synthesis
Level B
BLM:
Comprehension
DIF:
Level B
BLM:
Analysis
ANS:
A
DIF:
Level A
ANS:
16
DIF:
17.
18.
ANS:
BLM:
Knowledge
19.
ANS:
Substitution property of equality
DIF:
20.
Level A
BLM:
Knowledge
Level A
BLM:
Knowledge
Level A
BLM:
Knowledge
Level A
BLM:
Knowledge
Level A
BLM:
Knowledge
ANS:
DIF:
26.
Comprehension
ANS:
DIF:
25.
BLM:
ANS:
DIF:
24.
Level B
ANS:
Transitive Property of Equality
DIF:
23.
Comprehension
ANS:
Symmetric Property of Equality
DIF:
22.
BLM:
ANS:
Multiplication property of equality
DIF:
21.
Level B
ANS:
3. Linear Pair Postulate
5. Subtraction Property of Equality
DIF:
Level A
BLM:
Comprehension
27.
ANS:
DIF:
28.
Level A
BLM:
Comprehension
Level B
BLM:
Application
Level B
BLM:
Analysis
Level B
BLM:
Analysis
ANS:
DIF:
31.
Application
ANS:
DIF:
30.
BLM:
ANS:
Congruent Complements Theorem
DIF:
29.
Level B
ANS:
DIF:
32.
ANS:
33.
ANS:
96°
DIF:
34.
Level B
Level C
BLM:
Application
Level B
BLM:
Analysis
Level C
BLM:
Analysis
BLM:
BLM:
Knowledge
Knowledge
BLM:
Analysis
BLM:
Comprehension
ANS:
DIF:
36.
DIF:
ANS:
70
DIF:
35.
D
ANS:
a. 2
b.
11
a. DIF: Level A
b. DIF: Level B
37.
5
x  y  13
2
a.
b.
2
x y 5
5
DIF:
Level B
BLM:
Knowledge
38.
ANS:
D
DIF:
Level B
39.
ANS:
Level B
BLM:
Comprehension
Level B
BLM:
Comprehension

1
4
DIF:
40.
ANS:
neither
DIF:
41.
ANS:
Parallel; the lines have the same slope.
DIF:
42.
Level B
BLM:
Comprehension
Level B
BLM:
Comprehension
ANS:
DIF:
43.
ANS:
1
3
x-intercept: ( , 0)
1
2
y-intercept: (0,  )
DIF:
44.
Level B
BLM:
Comprehension
ANS:
y
10
10 x
–10
–10
DIF:
BLM:
Comprehension
Level B
BLM:
Comprehension
Level B
BLM:
Comprehension
Level B
BLM:
Comprehension
DIF:
Level B
BLM:
Comprehension
49.
ANS:
C
DIF:
Level B
50.
ANS:
SAS and SSS Congruence Postulates
45.
ANS:
72.4°, 71.4°, 36.2°
DIF:
46.
ANS:
67°
DIF:
47.
ANS:
101°
DIF:
48.
ANS:
x = 8; no
DIF:
51.
Level B
BLM:
Comprehension
ANS:
LM = 290; ASA Congruence Postulate
DIF:
52.
Level B
ANS:
Level A
BLM:
Comprehension
BLM:
Comprehension
12
DIF:
53.
Level B
BLM:
Analysis
Level B
BLM:
Analysis
Level C
BLM:
Synthesis
BLM:
Comprehension
ANS:
DIF:
56.
Application
ANS:
DIF:
55.
BLM:
ANS:
DIF:
54.
Level B
ANS:
WX = 13
DIF:
Level B
57. (x,y)
58. (x,y)
59. B
60.
61.
62.
 (x + 3, y – 6)
 (x – 3, y + 6)
AB ; 5,3
D
a.
b. P’(-1,6), Q’(0,9), R’(3,9)
c.
63.
64.
65.
 2,4
D
C
66.
67.
68.
C
69.
70.
71.
72.
73.
74.
75.
76.
77.
C
A” (1, 9), B” (-4, 7), C” (-1, 10)
D
Four lines
40 rotational symmetry and 9 lines of symmetry
D
1
7240
104 parts
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
About 12
18 feet, 21 feet, 24 feet
170
A
SAS Similarity Theorem
AA Similarity Postulate
similar,
19.0
B
20
90.
4
9
91.
3