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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
3. In the diagram, mLMN  54 .
BEGIN PART I (50 questions)
L
1. Use the diagram.
5
4
P
 2x  10 
1
3 2
 2x  
M
N
Which best describes the pair of angles 1
and 4 ?
What is the value of x?
(A) 27
(A) complementary
(B) 22
(B) linear pair
(C) 16
(C) supplementary
(D) 11
(D) vertical
4. In the diagram, Y is between X and Z,
and XZ  36 centimeters.
2. Use the diagram.
E
4b
F
X
b+6
Y
Z
A
B
C
What is the length of XY ?
D
(A) 24 cm
Which best describes the pair of angles
DBA and ABE ?
(B) 12 cm
(A) adjacent
(D) 8 cm
(C) 10 cm
(B) linear pair
(C) supplementary
(D) vertical
2010–2011
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
5. What is the distance between points
A  3, 12  and B  3, 4 ?
8. The lawyer presented all the facts of the
case in a logical order to the judge. What
type of reasoning did the lawyer use?
(A)
14
(A) conjecture
(B)
28
(B) deductive
(C) 10
(C) inductive
(D) 100
(D) intuitive
9. The teacher said, “If all the sides of a
triangle are congruent, then it is an
equilateral triangle.” A student replied, “If
it is not an equilateral triangle, then all the
sides are not congruent.” What type of
statement did the student use?
6. What are the coordinates of the midpoint
of AB with endpoints A 7, 2  and
B  5, 6  ?
(A) 1, 4 
 5 11 
(B)  ,

2 2 
(C)
(A) biconditional
(B) contrapositive
 6, 2
(C) converse
(D) inverse
(D) 12, 4 
10. What is the inverse of this statement?
7. In the pattern, the sides of each square
have a length of 1 unit.
If I am in my room, then I am happy.
(A) I am in my room, if and only if I am
happy.
Figure 1
Figure 2
(B) If I am happy, then I am in my room.
(C) If I am not happy, then I am not in
my room.
Figure 3
(D) If I am not in my room, then I am not
happy.
th
What is the perimeter of the 6 figure?
(A) 24
(B) 30
(C) 34
(D) 44
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
11. What is the converse of the statement?
13. In the diagram, line m is a transversal.
If Grandpa lives in California, then he
lives in the United States.
m
(A) If Grandpa lives in the United States,
then he lives in California.
1 4
3
2
5 8
6 7
(B) Grandpa lives in California, if and
only if he lives in the United States.
(C) If Grandpa does not live in
California, then he does not live in
the United States.
Which best describes the angle pair
4 and 8 ?
(D) If Grandpa does not live in the United
States, then he does not live in
California.
(A) supplementary
(B) corresponding
(C) alternate interior
(D) alternate exterior
12. Which is a counterexample to the
statement?
14. In the diagram, m n and t is a transversal.
All planets have moons.
m
(A) The planet Jupiter has many moons.
(B) The planet Mars has two moons.
 2x  20 
(C) The planet Mercury has no moons.
n
40°
t
(D) The planet Saturn has many moons.
What is the value of x?
(A) 10
(B) 30
(C) 60
(D) 140
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Geometry Honors 2010–2011 Semester 1 Exam — Released
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17. In order for lines m and n to be parallel,
what statement must be true?
15. In the diagram, m n and p q .
p
q
s
r
m
80°
x°
1
3
2
m
4
n
n
8 7
6 5
What is the value of x?
(A) 1 and 8 are corresponding
(A) 40
(B) 1 and 8 are complementary
(B) 80
(C) 3 and 6 are congruent
(C) 100
(D) 3 and 6 are supplementary
(D) 160
18. Which is a valid classification of a
triangle?
16. Use the diagram.
(A) acute equilateral
t
40°
(B) obtuse equiangular
 4y  
(C) right acute
m
(D) scalene isosceles
n
What value of y would show that line m
was parallel to line n?
(A) 50
(B) 40
(C) 35
(D) 10
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
19. Use the quadrilateral.
21. Use the triangles.
 6x  
 7 x  10 
 5 x  5 
85°
What is the value of x?
(A) 5
Which congruence postulate or theorem
proves these two triangles are congruent?
(B) 15
(C) 20
(A) angle-angle-side (AAS)
(D) 25
(B) side-angle-side (SAS)
20. In the diagram, JKLMN  RSTUV .
(C) side-side-angle (SSA)
(D) side-side-side (SSS)
J
22. In the diagram, NK  LM and 1  2 .
K
N
T
L
U
L
N
M
S
V
1
R
K
Which angle corresponds to M ?
2
M
Which congruence postulate or theorem
would prove LMK  NKM ?
(A) R
(B) S
(A) angle-side-angle (ASA)
(C) T
(B) side-angle-side (SAS)
(D) U
(C) side-side-angle (SSA)
(D) side-side-side (SSS)
2010–2011
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
23. Given that JKL  RST , JK  3z  21 ,
KL  2z  25 , LJ  21  3z , and
ST  5z  31 , what is the value of z?
25. The statements for a proof are given
below.
Given:
(A) 5
NO  PM
NO PM
(B) 2
Prove: OP  MN
(C) 1
(D) 2
O
24. Given that PQR  XYZ ,
mP   7n  5  , mQ   3n  5  , and
P
N
mZ  30 . What is the value of n?
M
4
(A) 3
7
(B) 11
Proof:
2
3
(C) 15
(D) 18
STATEMENTS
REASONS
1. NO  PM , NO PM
2. ONP  MPN
1. Given
3. NP  NP
4. MPN  ONP
2.
3.
4.
5. OP  MN
5.
What reason makes the statement in Step 4
true?
(A) side-angle-side (SAS)
(B) side-side-side (SSS)
(C) corresponding parts of congruent
triangles are congruent (CPCTC)
(D) angle-side-angle (ASA)
2010–2011
Clark County School District
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
27. Given that DEF  LMN ,
mF   4x  8  , mM   5x  7   , and
26. The statements for a proof are given
below.
Given: I is the midpoint of
K  G
Prove: GH
D   x  15  , what is the value of x?
GK
(A) 1
 KJ
(B) 2
(C) 6
K
H
(D) 15
I
28. In triangle PQR, QP  RP and
mR  63 .
J
G
P
Proof:
STATEMENTS
REASONS
1. I is the midpoint of GK
K  G
2. HIG  JIK
1. Given
3. GI  KI
4. HIG  JIK
5. GH  KJ
Q
2.
3.
R
What is the measure of P ?
4.
5.
(A) 27°
(B) 54°
What is the reason for the 5th statement?
(C) 63°
(A) definition of a midpoint
(D) 117°
(B) angle-side-angle (ASA)
(C) prove
(D) corresponding parts of congruent
triangles are congruent. (CPCTC)
2010–2011
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Geometry Honors 2010–2011 Semester 1 Exam — Released
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29. Three towns form a triangle on the map.
32. Which list of three lengths would form a
triangle?
Jasper
34 miles
(A) 4, 4, 7
18 miles
Alta
x
(B) 4, 5, 10
Washington
(C) 5, 6, 12
Which value of x is NOT a possible
distance between Alta and Washington?
(D) 6, 6, 12
33. BE is a median of ABC .
(A) 10 miles
(B) 20 miles
A
(C) 30 miles
8
(D) 40 miles
30. Given A 2, 5 and B  4,  2  . What is
the distance from A to B?
E
10
7
B
C
(A)
13
(B)
45
(C)
53
(B) 8
(D)
85
(C) 10
What is the length of AC ?
(A) 6
(D) 14
31. In ABC , AB = 6 centimeters,
BC = 9 centimeters, and
CA = 5 centimeters. Which list shows the
angles in order from largest to smallest?
(A) B, C , A
(B) B, A, C
(C) A, B, C
(D) A, C , B
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
34. In EFG , HI , IJ , and JH are
midsegments, GJ = 6 centimeters, and
EI = 8 centimeters.
36. How many sides does a decagon have?
(A) 6
(B) 8
G
(C) 10
6 cm
H
(D) 12
J
37. Which group of figures are all polygons?
E
8 cm
I
F
(A)
What is the length of EF ?
(A) 10 cm
(B)
(B) 14 cm
(C) 16 cm
(D) 20 cm
(C)
35. Use the diagram.
(D)
38. What is the sum of the measures of the
interior angles of this polygon?
What is the name of the point of
concurrency in this triangle?
(A) centroid
(B) circumcenter
(A) 360
(C) incenter
(B) 540
(D) orthocenter
(C) 720
(D) 1080
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
39. What is the sum of the exterior angles of a
polygon?
42. Which statement is true?
(A) All parallelograms have only one pair
of parallel sides.
(A) 180
(B) All parallelograms have
complimentary consecutive angles.
(B) 360
(C) 540
(C) All parallelograms have diagonals
that bisect each other.
(D) 720
(D) All parallelograms have four
congruent sides.
40. The figure below is a rhombus.
43. Which statement is true about all isosceles
trapezoids?
5x + 45
(A) Both pairs of opposite sides are
congruent.
7x + 15
What is the value of x?
(B) Both pairs of opposite sides are
parallel.
(A) 2.5
(C) One pair of opposite sides is both
parallel and congruent.
(B) 10
(C) 15
(D) One pair of opposite sides is parallel,
and the other pair is congruent.
(D) 30
41. What is the measure of each exterior angle
of a regular decagon?
(A) 36°
(B) 45°
(C) 135°
(D) 144°
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Geometry Honors 2010–2011 Semester 1 Exam — Released
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44. In the diagram, BCA  XZY . Which
statement must be true?
X
46. A regular polygon has interior angles that
measure 135 . How many sides does this
polygon have?
Z
120°
(A) 4
(B) 6
40°
(C) 8
Y
B
(D) 10
47. Use the diagram.
10 cm
8cm
C
A
93°
x°
(A) mX  40
(B) XY  8cm
56°
91°
(C) XZ  8cm
(D) ZY  8cm
What is the value of x?
(A) 120
45. Figure GHIJ is a parallelogram.
G
(B) 128
H
 2x  25 
(C) 180
(D) 240
J
 x  35 
I
What is the value of x?
(A) 10
(B) 40
(C) 60
(D) 80
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Geometry Honors 2010–2011 Semester 1 Exam — Released
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48. Given that FGH is an equilateral
triangle, what is the measure of an acute
angle of the triangle?
(A) 45°
(B) 60°
(C) 90°
(D) 120°
49. Using the table, what is the nth term of the
sequence?
1
4
2
8
3
12
4
16
…
…
n
?
(A) n  4
(B) 3n  2
(C) 4n
(D) 4n  3
50. Austin went to track practice after school
on Monday, Tuesday, and Wednesday.
Using inductive reasoning, what
conclusion can you make about his
Thursday after-school activity?
(A) Austin will go home.
(B) Austin will go to swim practice.
(C) Austin will go to a meeting.
(D) Austin will go to track practice.
END PART I
GO ON TO PART II
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Note: Diagrams on this exam are not necessarily drawn to scale.
3. UV has an endpoint at U  7, 5 , and the
BEGIN PART II (10 questions)
midpoint is at M  2, 1 . What are the
coordinates of endpoint V?
1. In EFG, H , I , and J are midpoints.
G
H
E
(A)
 12, 10
(B)
 4, 3
(C)
 3, 3
(D)
 4, 5
J
K
F
I
4. Rectangle MHRG has vertices
M  5, 2 , H 1, 10 , R  5, 7  , and
If GI = 36, what is KG?
(A) 6
G  1, 1 . What is the length of diagonal
(B) 12
MR ?
(C) 18
(D) 24
2. Based on the dimensions given in the
diagram, what is the longest line segment
in the diagram?
(A)
15
(B)
81
(C)
125
(D)
181
P
R
Q
70°
55°
5. In an indirect proof, after assuming the
opposite of the “Proof Statement”
(conclusion), the next step in the process
is to
55°
65°
60°
55°
80°
T
60°
(A) find a contradiction
40°
(B) prove the false assumption
S
(C) prove the given information
(A) QS
(D) use CPCTC
(B) RS
(C) TQ
(D) TS
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Geometry Honors 2010–2011 Semester 1 Exam — Released
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8. The nth term of a sequence is  3n  1 . If
the value of a term is 400, what is the next
term?
6. To begin an indirect proof, an initial
assumption is made. If one were trying to
prove that x = 9, what should be the initial
assumption?
2
(A) x = 9
(A) 8
(B) x < 9
(B) 289
(C) x > 9
(C) 409
(D) x  9
(D) 529
9. Given points A 4, 16  and B  x, 4 ,
what is a possible value of x if the length
of AB is 13?
7. In the diagram, which coordinates would
result in a kite?
(A) –5
(B) –1
(C) 5
(D) 12
10. In isosceles triangle HMS, M is the
vertex angle. If mM   2  x  3   and
mH   9 x  7   , what is mM ?
(A) 10°
(A) 10, 1
(B) 22°
(B)
9, 2
(C) 79°
 7, 11
(D) 80°
(C)
(D)
 6, 5
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Geometry Honors 2010–2011 Semester 1 Exam — Released
Free Response
1. This question obsolete as of 2011–2012. See new test specifications and practice questions.
2. This question obsolete as of 2011–2012. See new test specifications and practice questions.
3. This question obsolete as of 2011–2012. See new test specifications and practice questions.
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