Geometry Semester 1 Practice Exam
1. Use the figure below.
3. In the diagram below, m∠ABC = 42° .
A
2
1
3
4
5
D
( 7 x + 2) °
( 3x ) °
B
Which best describes the pair of angles:
∠ 4 and ∠ 5 ?
C
What is the value of x?
A. vertical
B. adjacent
A. 2
C. linear pair
B. 3
D. complementary
C. 4
2. In the diagram below, ∠DBF , ∠EBC ,
and ∠EBA are right angles.
E
1
2
D. 4
2
5
F
4. In the figure below, Y is between X and Z
and XZ = 40 cm.
D
3
2
1
A
B
a
3a + 8
4
X
C
Y
Z
What is the value of a?
Which best describes the pair of angles:
∠1 and ∠ 4 ?
A. 4
A. vertical
B. 8
B. adjacent
C. 12
C. supplementary
D. 16
D. complementary
5. What is the distance between points
A ( −2, −6 ) and B ( −2, −3 ) ?
A. 3
B.
41
C. 9
D.
2008–2009
Clark County School District
1
Revised 12/17/2009
89
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Geometry Semester 1 Practice Exam
6. What are the coordinates of the midpoint
of the segment joining the points
A ( −3, −4 ) and B ( 4, 2 ) ?
9. All donks are widgets. Which statement
can be written using the rules of logic?
A. A donk is a widget if and only if it is an
object.
⎛ 1 ⎞
A. ⎜ −3 ,3 ⎟
⎝ 2 ⎠
B. An object is a donk if and only if it is a
widget.
⎛ 1
⎞
B. ⎜ − , −1⎟
⎝ 2
⎠
C. If an object is a widget, then it is a donk.
D. If an object is a donk, then it is a widget.
⎛1
⎞
C. ⎜ , −1⎟
⎝2
⎠
10. Which statement is the inverse of:
If x = 5, then x > 3?
⎛1
⎞
D. ⎜ , −3 ⎟
⎝2
⎠
A. If x = 3 , then x < 5 .
B. If x ≤ 3 , then x ≠ 5 .
7. In the pattern below, the sides of each
regular hexagon have a length of 1 unit.
C. If x > 3 , then x = 5 .
D. If x ≠ 5 , then x ≤ 3 .
11. Which is a valid counterexample of the
converse of the statement: If Hedley lives
in North Las Vegas, then he lives in
Nevada?
What is the perimeter of the 5th figure?
A. 18 units
B. 22 units
A. Hedley lives in Phoenix.
C. 26 units
B. Hedley lives in California.
D. 30 units
C. Hedley lives in Reno.
D. Hedley lives in the United States.
8. In the scientific method, after one makes
a conjecture, one tests the conjecture.
What type of reasoning is used?
12. Which is the contrapositive to the
statement: If n is odd, then n2 + 2n + 1 is
even.
A. conclusive
B. deductive
A. If n 2 + 2n + 1 is odd, then n is even.
C. inductive
B. If n 2 + 2n + 1 is even, then n is odd.
D. scientific
C. If n is even, then n 2 + 2n + 1 is odd.
D. If n is even, then n 2 + 2n + 1 is even.
2008–2009
Clark County School District
2
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
15. In the figure below, n & m and l is a
transversal.
13. In the figure below, line m is a
transversal.
m
1
x°
n
117°
2
m
l
Which best describes the pair of angles:
∠1 and ∠ 2 ?
What is the value of x?
A. alternate exterior
A. 180
B. alternate interior
B. 117
C. corresponding
C. 63
D. vertical
D. 53
14. In the figure below, n & m and l is a
transversal.
16. In the figure below, m∠FGH = 65° .
( 2 x − 17 ) °
l
64°
n
F
G
( 4 x − 16 ) °
m
65°
H
m
What value of x would make line l
parallel to line m?
l
What is the value of x?
A. 41
A. 33
B. 49
B. 29
C. 65
C. 20
D. 66
D. 16
2008–2009
Clark County School District
3
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
17. In the figure below, lines l and m are
parallel.
20. In the figures below,
ABCDEF ≅ RSTUVW .
B
5
1
6
2
A
l
3
4
7
C
8
F
m
D
Which statement is true?
E
A. ∠1 and ∠3 are congruent.
W
B. ∠1 and ∠8 are supplementary.
R
C. ∠2 and ∠4 are supplementary.
D. ∠6 and ∠7 are congruent.
V
18. Which is a valid classification for a
triangle?
S
U
A. Acute right
B. Isosceles scalene
T
C. Isosceles right
Which side of RSTUVW corresponds
to DE ?
D. Obtuse equiangular
A. RW
19. Use the triangle below.
B. SR
x°
C. UT
( 3 x + 3) °
D. UV
45°
What is the value of x?
A. 29
B. 33
C. 44
D. 49
2008–2009
Clark County School District
4
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
23. Given that ΔRST ≅ ΔXYZ ,
m∠R = ( 6n + 1) ° , m∠Y = 108° , and
21. Use the triangles below.
m∠Z = ( 9n − 4 ) ° , what is the value of n?
A.
5
3
B. 5
Which congruence postulate or theorem
would prove that these two triangles are
congruent?
C.
107
6
D.
179
6
24. Given that ΔPQR ≅ ΔJKL , PQ = 4 x + 12 ,
JK = 7 x − 6 , KL = 2 x + 17 , and
JL = 5 x − 7 , what is the value of x?
A. angle-angle-side
B. angle-side-angle
A. 2
C. side-angle-side
1
2
D. side-side-side
B. 6
22. In the diagram below, AB ≅ DC and
AB & DC .
C. 12
A
4
7
D. 19
C
E
B
D
Which congruence postulate or theorem
would prove that these two triangles are
congruent?
A. side-side-side
B. angle-angle-angle
C. side-angle-side
D. angle-side-angle
2008–2009
Clark County School District
5
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
25. The statements for a proof are given
below.
26. The statements for a proof are given
below.
Given: Parallelogram ABCD
BX ≅ DY
Prove:
Given:
AB ≅ FD
∠B ≅ ∠D
∠A ≅ ∠F
Prove:
BC ≅ DE
∠BAX ≅ ∠YCD
X
B
C
E
B
A
D
Y
D
A
Proof:
STATEMENTS
1. Parallelogram ABCD
BX ≅ DY
2. ∠B ≅ ∠D
3. AB ≅ DC
4. ΔABX ≅ ΔCDY
5. ∠1 ≅ ∠ 2
C
REASONS
1. Given
Proof:
2.
3.
4.
5.
STATEMENTS
1.
2.
3.
4.
What is the reason that the statement in
Step 4 is true?
AB ≅ FD
∠B ≅ ∠ D
∠A ≅ ∠ F
ΔABC ≅ ΔFDE
5. BC ≅ DE
F
REASONS
1. Given
2. Given
3. Given
4. ______
5. Corresponding Parts
of Congruent Triangles
are Congruent
A. side-angle-side
What is the missing reason that would
complete this proof?
B. angle-side-angle
C. Opposite sides of a parallelogram are
congruent.
A. side-side-side
B. side-angle-side
D. Corresponding angles of congruent triangles
are congruent.
C. angle-side-angle
D. angle-angle-side
2008–2009
Clark County School District
6
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
27. Given that ΔDEF ≅ ΔLMN ,
m∠D = ( 2 x + 15 ) ° , m∠L = ⎡⎣ 3 ( x − 2 ) ⎤⎦ ° ,
29. Three towns form a triangle on the map
below.
and DF = 4( x − 17) , what is LN?
Geometria
A. 16
9 miles
B. 21
C. 57
D. 67
Euclid
Euler
7 miles
Which statement does NOT represent
possible distances between Euclid and
Geometria?
28. In the isosceles triangle below,
m∠H = 137° .
F
A. Between 2 and 7 miles apart.
137°
G
B. Between 7 and 9 miles apart.
C. Between 9 and 16 miles apart.
H
What is the measure of ∠F ?
D. Between 49 and 81 miles apart.
30. The ΔRST is constructed with vertices
R ( −5, 2 ) , S ( 4,1) , and T ( 2, −1) . What is
A. 21.5°
B. 26.5°
C. 43°
the length of ST ?
D. 53°
A.
90
B.
58
C.
8
D. 2
31. In ΔABC , ∠B is a right angle and
m∠A = 40° . Which list shows the sides in
order from longest to shortest?
A. AB, BC , AC
B. BC , AB, AC
C. AC , BC , AB
D. AC , AB, BC
2008–2009
Clark County School District
7
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
34. In ΔBCD , SR is a midsegment, and
SQ & DC .
32. A triangle has two sides that have lengths
of 7 cm and 17 cm. Which could
represent the length of the third side of
the triangle?
B
A. 24 cm
B. 18 cm
Q
S
C. 10 cm
5
D. 7 cm
D
33. The triangle below contains three
midsegments.
12
C
R
What is the length of QC ?
A. 34
B. 26
x
C. 17
14
11
D. 13
z
9
35. The triangle below shows a point of
concurrency. Lines l, m, and n, are
perpendicular bisectors of the triangle’s
sides.
y
What are the values of x, y, and z?
m
A. x = 9, y = 22, z = 7
B. x = 9, y = 11, z = 14
l
C. x = 9, y = 22, z = 14
D. x = 18, y = 11, z = 7
n
What is the name of the point of
concurrency in the triangle?
A. centroid
B. incenter
C. orthocenter
D. circumcenter
2008–2009
Clark County School District
8
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
36. How many sides does a nonagon have?
38. A hexagon is shown below.
A. 7
a°
B. 9
100°
C. 11
D. 19
150°
37. Which figure is a polygon?
What is the value of a?
A.
A. 90
B. 100
C. 130
B.
D. 150
39. Use the figure below.
C.
130°
60°
x°
40°
D.
What is the value of x?
A. 70
B. 60
C. 50
D. 40
2008–2009
Clark County School District
9
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
44. In the figure below, ΔKLM ≅ ΔABC .
40. Parallelogram ABCD is given below.
11x + 9
A
31
D
6(x + 4)
A
L
B
8 cm
C
47°
What is the value of x?
K
10 cm
M
C
53°
A. 2
B
B. 3
Which statement must be true?
C. 6
A. AC = 8cm
D. 16
B. BC = 6cm
41. What is the measure of each exterior
angle of a regular hexagon?
C. m∠A = 53°
D. m∠C = 80°
A. 60°
45. Use the rhombus below.
B. 90°
C. 120°
B
A
65°
D. 135°
42. Which statement is true about a kite?
E
A. A kite has 4 congruent sides.
B. A kite has 2 pairs of parallel sides.
C. A kite has perpendicular diagonals.
C
D. A kite has congruent diagonals.
D
What is m∠CDE ?
43. Which statement below is true about an
isosceles trapezoid?
A. 25°
A. Both pairs of opposite sides are parallel.
C. 90°
B. Both pairs of opposite sides are congruent.
D. 115°
B. 65°
C. One pair of opposite sides is congruent and
the other is parallel.
D. One pair of opposite sides is both parallel
and congruent.
2008–2009
Clark County School District
10
Revised 12/17/2009
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Geometry Semester 1 Practice Exam
46. A regular polygon has interior angles that
measure 144°. How many sides does this
polygon have?
49. What is the nth term of the sequence
1, 4, 9, 16, 25 …?
A. 6
A. 2n − 1
B. 8
B. n + 3
C. 10
C. n 2
D. 12
D. 3n 2
47. Use the figure below.
50. Geometric figures are displayed on a
computer screen in the following order:
triangle, concave quadrilateral, convex
pentagon, concave hexagon. Using
inductive reasoning, what prediction can
be made about the next figure?
75°
A. It will be a concave heptagon.
41°
x°
B. It will be a convex heptagon.
C. It will be a convex polygon, but the type
cannot be predicted.
What is the value of x?
D. It will be a polygon, but no other details
about it can be predicted.
A. 64
B. 74
C. 116
D. 126
48. Given that ΔFGH is an isosceles right
triangle, what is the measure of an acute
angle of the triangle?
A. 45°
B. 60°
C. 90°
D. 120°
2008–2009
Clark County School District
11
Revised 12/17/2009
Geometry 2011–2012 Semester 1
Free Response Practice Exam
OK
Note: Diagrams on this exam are not necessarily drawn to scale.
1. Use the diagram to find the measure of the
following angles, given that m & n :
m∠1 = ________
m∠2 = ________
m∠3 = ________
m∠4 = ________
Calculators
allowed
m
n
105°
1
2
5
4
40°
m∠5 = ________
3
2. Using the figure provided, write a geometric proof.
A
Given: ΔACD is isosceles with vertex A
∠1 ≅ ∠3
2
Prove: AB & CD
3
4
C
D
3. Use coordinate geometry to prove that ΔABC ≅ ΔSTR .
y
B
T
A
C
x
S
R
2011–2012
Clark County School District
1
Revised 01/11/2012
B
1
GEOMETRY SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY Free Response # 1 2 3 Œ
Œ
Œ
Œ
Œ
Œ
Œ
Œ
Œ
Syllabus Objectives 1.1–1.10 3.1–3.8 4.2 2.1–2.11 4.1–4.12 1.1–1.10 2.1–2.11 3.1–3.8 4.1–4.12 Course Concepts / Objectives Points, Lines, Planes, and Angles Parallel and Perpendicular Lines Solve problems applying the triangle sum theorems. Logic, Reasoning, and Proof Triangle Relationships Points, Lines, Planes, and Angles Logic, Reasoning, and Proof Parallel and Perpendicular Lines Triangle Relationships NV State Standards 3.12.3 4.12.1–4.12.9 3.12.5
4.12.1–4.12.9 3.12.3 3.12.5 4.12.1–4.12.9 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Objective Classify pairs of angles. Classify pairs of angles. Solve segment and angle problems using algebraic techniques. Solve segment and angle problems using algebraic techniques. Find the distance between two points. Find the midpoint of a segment. Justify conjectures and solve problems using inductive reasoning. Differentiate between deductive and inductive reasoning. Analyze conditional or bi‐conditional statements.
Write and analyze the converse, inverse, and contrapositive of a statement. Write and analyze the converse, inverse, and contrapositive of a statement. Find counterexamples to disprove mathematical statements. Analyze relationships when two lines are cut by a transversal. Solve problems which involve parallel or perpendicular lines using algebraic techniques. Solve problems which involve parallel or perpendicular lines using algebraic techniques. Solve problems which involve parallel or perpendicular lines using algebraic techniques. Write proofs relating to parallel and perpendicular lines. Classify triangles by sides and/or angles. Solve problems involving properties of polygons.
Analyze the relationships between congruent figures.
Prove that two triangles are congruent. Prove that two triangles are congruent. 2011–2012 Clark County School District Syllabus Objective 1.5
1.5
NV State Standard 4.12.6
4.12.6
Key C
D
1.6 4.12.6 C 1.6 4.12.6 B 1.8
1.9
3.12.3
3.12.3
A
C
2.2 4.12.9 B 2.3 4.12.9 B 2.6
4.12.9
D
2.7 4.12.9 D 2.7 4.12.9 C 2.9 4.12.9 A 3.2 4.12.6 A 3.3 4.12.6 C 3.3 4.12.6 C 3.3 4.12.6 D 3.4 4.12.9 A 4.1
5.6
4.3
4.6
4.6
4.12.1
4.12.6
4.12.6
4.12.9
4.12.6
C
B
D
A
D
Page 1 of 2 Revised: 05/25/2011 GEOMETRY SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY # 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Objective Solve problems related to congruent triangles using algebraic techniques. Solve problems related to congruent triangles using algebraic techniques. Prove that two triangles are congruent. Justify congruence using corresponding parts of congruent triangles. Solve problems related to congruent triangles using algebraic techniques. Prove and use the properties of isosceles and/or equilateral triangles. Solve problems applying the properties of triangle inequalities. Find the distance between two points. Solve problems applying the properties of triangle inequalities. Solve problems applying the properties of triangle inequalities. Apply special segment properties to solve problems.
Apply special segment properties to solve problems.
Explore the points of concurrency and their special relationships. Differentiate among polygons by their attributes.
Differentiate among polygons by their attributes.
Find the sum of the measures of the interior angles of a polygon. Solve problems involving properties of polygons.
Solve problems involving properties of special quadrilaterals. Find the measures of interior, exterior, and central angles of a given regular polygon. Solve problems involving properties of special quadrilaterals. Solve problems involving properties of special quadrilaterals. Justify congruence using corresponding parts of congruent triangles. Solve problems involving properties of polygons.
Find the measures of interior, exterior, and central angles of a given regular polygon. Solve problems involving properties of polygons.
Prove and use the properties of isosceles and/or equilateral triangles. Justify conjectures and solve problems using inductive reasoning. Justify conjectures and solve problems using inductive reasoning. Syllabus Objective NV State Standard Key 4.5 4.12.1 B 4.5 4.12.6 B 4.6
4.12.9
A
4.4 4.12.9 C 4.5 4.12.1 A 4.7 4.12.1 A 4.11 4.12.7 D 1.8
3.12.3
C
4.11 4.12.7 D 4.11 4.12.7 B 4.13
4.13
4.12.1
4.12.7
A
D
4.14 4.12.1 D 5.1
5.1
4.12.1
4.12.1
B
D
5.3 4.12.6 C 5.6
4.12.6
A
5.4 4.12.1 B 5.8 4.12.6 A 5.4 4.12.1 C 5.4 4.12.1 C 4.4 4.12.9 D 5.6
4.12.6
B
5.8 4.12.6 C 5.6
4.12.1
C
4.7 4.12.9 A 2.2 4.12.9 C 2.2 4.12.9 B 2011–2012 Clark County School District Page 2 of 2 Revised: 05/25/2011