Download Intuitive Geometry S1 Practice

Intuitive 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
2008–2009
Clark County School District
1
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
5. What is the distance between points
A ( −2, −6 ) and B ( −2, −3 ) ?
d=
( x2 − x1 ) + ( y2 − y1 )
2
8. What type of reasoning is based on
definitions, postulates, and theorems?
A. deductive
2
B. hypothetical
A.
89
C. inductive
B.
41
D. scientific
C. 9
9. Which statement is the inverse of: If an
angle is acute, then it is not obtuse?
D. 3
A. If an angle is obtuse, then it is not acute.
6. What are the coordinates of the midpoint
of the segment joining the points
A ( −3, −4 ) and B ( 4, 2 ) ?
B. If an angle is acute, then it is obtuse.
C. If an angle is not obtuse, then it is acute.
⎛ x + x2 y1 + y2 ⎞
Midpoint: ⎜ 1
,
2 ⎟⎠
⎝ 2
D. If an angle is not acute, then it is obtuse.
10. In the figure below line m is a transversal.
⎛ 1 ⎞
A. ⎜ −3 ,3 ⎟
⎝ 2 ⎠
1
⎛ 1
⎞
B. ⎜ − , −1⎟
⎝ 2
⎠
⎛1
⎞
C. ⎜ , −1⎟
⎝2
⎠
2
m
⎛1
⎞
D. ⎜ , −3 ⎟
⎝2
⎠
Which best describes the pair of angles:
∠1 and ∠ 2 ?
A. alternate exterior
7. In the pattern below, the sides of each
regular hexagon have a length of 1 unit.
B. alternate interior
C. corresponding
D. vertical
What is the perimeter of the 5th figure?
A. 18 units
B. 22 units
C. 26 units
D. 30 units
2008–2009
Clark County School District
2
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
13. In the figure below, m∠FGH = 65° .
11. In the figure below, n & m and l is a
transversal.
( 2 x − 17 ) °
l
64°
F
G
n
65°
m
( 4 x − 16 ) °
H
m
What value of x would make line l
parallel to line m?
l
A. 41
What is the value of x?
B. 49
A. 33
C. 65
B. 29
D. 66
C. 20
D. 16
14. In the figure below, lines l and m are
parallel.
12. In the figure below, n & m and l is a
transversal.
m
5
1
6
2
x°
l
3
n
4
117°
7
8
m
Which statement is true considering the
given information?
l
A. ∠1 and ∠3 are congruent.
What is the value of x?
B. ∠1 and ∠8 are supplementary.
A. 180
C. ∠2 and ∠4 are supplementary.
B. 117
D. ∠6 and ∠7 are congruent.
C. 63
D. 53
2008–2009
Clark County School District
3
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
15. Which is a valid classification for a
triangle?
17. In the figures below,
ABCDEF ≅ RSTUVW .
A. Acute right
B
B. Isosceles scalene
A
C. Isosceles right
D. Obtuse equiangular
C
F
16. Use the triangle below.
D
x°
E
W
( 3 x + 3) °
R
45°
V
What is the value of x?
S
A. 29
U
B. 33
C. 44
D. 49
T
Which side of RSTUVW corresponds
to DE ?
A. RW
B. SR
C. UT
D. UV
2008–2009
Clark County School District
4
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
20. Given that ΔRST ≅ ΔXYZ ,
m∠R = ( 7 n + 3 ) ° , and m∠X = ( 8n − 2 ) ° ,
18. Use the triangles below.
what is the value of n?
A. 3
B. 5
C. 12
D. 38
21. Given that ΔPQR ≅ ΔJKL , PQ = 4 x + 12 ,
JK = 44 , KL = 24 , and JL = 32 , what is
the value of x?
Which congruence postulate or theorem
would prove that these two triangles are
congruent?
A. 3
B. 5
A. angle-angle-side
C. 8
B. angle-side-angle
D. 22
C. side-angle-side
22. In the isosceles triangle below,
m∠H = 137° .
D. side-side-side
19. In the diagram below, AB ≅ DC and
AB & DC .
F
137°
A
C
G
H
What is the measure of ∠F ?
E
A. 21.5°
B
B. 26.5°
D
C. 43°
Which congruence postulate or theorem
would prove that these two triangles are
congruent?
D. 53°
A. angle-angle-angle
B. angle-side-angle
C. side-side-side
D. side-angle-side
2008–2009
Clark County School District
5
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
23. In ΔABC , ∠B is a right angle and
m∠A = 40° . Which list shows the sides in
order from longest to shortest?
26. Which figure is a polygon?
A.
A. AB, BC , AC
B. BC , AB, AC
C. AC , BC , AB
B.
D. AC , AB, BC
24. 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?
C.
A. 24 cm
D.
B. 18 cm
C. 10 cm
D. 7 cm
27. A hexagon is shown below.
25. How many sides does a nonagon have?
a°
A. 7
100°
B. 9
C. 11
150°
D. 19
What is the value of a?
A. 90
B. 100
C. 130
D. 150
2008–2009
Clark County School District
6
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
28. Parallelogram ABCD is given below.
42
A
32. Use the rhombus below.
B
B
A
65°
24
D
3(x + 6)
C
E
What is the value of x?
A. 6
B. 8
C
C. 12
D
What is m∠CDE ?
D. 16
A. 25°
B. 65°
29. What is the measure of each exterior
angle of a regular hexagon?
C. 90°
A. 60°
D. 115°
B. 90°
33. What is the measure of one interior angle
of a regular octagon?
C. 120°
D. 135°
A. 45°
B. 135°
30. Which statement is true about a kite?
C. 180°
A. A kite has 4 congruent sides.
D. 1080°
B. A kite has 2 pairs of parallel sides.
C. A kite has congruent diagonals.
D. A kite has perpendicular diagonals.
34. Given that ΔFGH is an isosceles right
triangle, what is the measure of an acute
angle of the triangle?
31. Which statement below is true about an
isosceles trapezoid?
A. 45°
B. 60°
A. Both pairs of opposite sides are parallel.
C. 90°
B. Both pairs of opposite sides are congruent.
D. 120°
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
7
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
35. What is the 6th term of the sequence
1, 2, 4, 8, …?
38. What property below is true for both a
rectangle and a rhombus?
A. 12
A. Diagonals bisect each other.
B. 16
B. Diagonals bisect the angles.
C. 32
C. Diagonals are congruent.
D. 645
D. Diagonals are perpendicular.
36. 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?
39. A rectangle ALWAYS has which of the
following properties?
A. It will be a concave heptagon.
D. Only one pair of congruent sides.
A. Diagonals are congruent.
B. Diagonals are perpendicular.
C. Four congruent sides.
B. It will be a convex heptagon.
40. If a run is scored in baseball, then a
player has crossed home plate. This is an
example of what kind of reasoning?
C. It will be a convex polygon, but the type
cannot be predicted.
D. It will be a polygon, but no other details
about it can be predicted.
A. scientific
B. inductive
37. What is the slope of the line through
points A ( −3, −4 ) and B ( 7, −2 ) ?
C. deductive
D. conclusion
slope =
A.
y2 − y1
x2 − x1
41. In the conditional statement, “If it is
rainy, then it is cloudy,” what is the
underlined portion called?
5
1
A. conclusion
1
B.
5
B. converse
C. inverse
1
C. −
5
D. −
D. hypothesis
5
1
2008–2009
Clark County School District
8
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
42. Chan graphs a line with the equation
y = −3 x − 7 . What is the slope of a line
parallel to Chan’s line?
44. Using the following conditionals:
If I do my homework, then I will pass the
test.
A. −
1
7
B. −
1
3
C. −
3
1
A. If I get my cell phone back, then I passed the
test.
D. −
7
1
B. If I passed the test, then I did my homework.
If I pass the test, then I will get my cell
phone back.
What conclusion can be logically
deduced?
C. If I get my cell phone back, then I will call
my friend.
2
43. A line has a slope of − . What is the
3
slope of a line that is perpendicular to it?
D. If I do my homework, then I will get my cell
phone back.
45. Given the angle below:
3
A. −
2
B. −
B
2
3
D
A
2
C.
3
C
3
D.
2
JJJG
Which term best describes AD in
relation to ∠BAC ?
A. angle bisector
B. exterior
C. side
D. vertex
2008–2009
Clark County School District
9
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
46. Use the diagram below:
47. Use the diagram below:
3
4
3
2
5
4
1
2
5
1
Which statement justifies the conclusion
that m∠5 = m∠ 3 + m∠4?
Which statement justifies the conclusion
that m∠ 2 + m∠ 5 = 180° ?
A. Exterior Angle Theorem
A. Exterior Angle Theorem
B. Linear Pair Theorem
B. Linear Pair Theorem
C. Triangle Sum Theorem
C. Triangle Sum Theorem
D. Vertical Angle Theorem
D. Vertical Angle Theorem
48. Use the protractor pictured below.
X
Z
Y
What is the measure of ∠XYZ ?
A. 55°
B. 65°
C. 125°
D. 135°
2008–2009
Clark County School District
10
Revised 07/22/2009
GO ON
Intuitive Geometry Semester 1 Practice Exam
49. Given ΔABC :
B
E
A
C
D
What type of special segment is DE ?
A. Altitude
B. Angle Bisector
C. Median
D. Perpendicular Bisector
50. Given ΔKML :
K
L
M
X
What type of special segment is XL ?
A. Perpendicular Bisector
B. Median
C. Angle Bisector
D. Altitude
2008–2009
Clark County School District
11
Revised 07/22/2009
Intuitive 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
1 2
3 4
Given: ∠3 and ∠5 are supplementary.
5 6
7 8
C
Prove: AB & CD
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 05/25/2011
B
D
INTUITIVE GEOMETRY SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY Free Response # Syllabus Objectives 4.1–4.12 6.5 3.1–3.9 4.1–4.15 6.1–6.11 6.13–6.15 3.1–3.9 4.1–4.15 5.1–5.7 6.1–6.11 6.13–6.15 Course Concepts / Objectives 1 Œ Lines and Angles Œ Solve problems involving angles of a triangle. 2 Œ Reasoning Skills and Logic Œ Lines and Angles Œ Triangles 3 Œ
Œ
Œ
Œ
Reasoning Skills and Logic Lines and Angles Coordinate Geometry Triangles 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 Objective Classify pairs of angles. Classify pairs of angles. Solve angle‐measure problems. Formulate strategies for determining distance between two points. Formulate strategies for determining distance between two points. Formulate strategies for determining the midpoint of a segment. Explore geometric or algebraic relationships using patterns. Compare deductive and inductive arguments.
Compare deductive and inductive arguments.
Solve problems using postulates & theorems related to parallel and perpendicular lines. Solve problems using postulates & theorems related to parallel and perpendicular lines. Solve problems using postulates & theorems related to parallel and perpendicular lines. Explore conditions which guarantee parallel and perpendicular lines. Justify conclusions to problems on parallel & perpendicular lines using postulates and theorems. Classify triangles by angle or side measure. Solve problems involving angles of a triangle.
Solve and prove problems using the theorems and postulates for congruence. Solve and prove problems using the theorems and postulates for congruence. Solve and prove problems using the theorems and postulates for congruence. Syllabus Objective 4.7
4.7
4.10
NV State Standard 4.12.6
4.12.6
4.12.6
Key C
D
C
5.1 4.12.6 B 5.1 3.12.3 D 5.3 3.12.3 C 1.5 4.12.9 B 3.8
3.8
4.12.9
4.12.9
A
D
4.3 4.12.6 A 4.3 4.12.6 C 4.3 4.12.6 C 4.5 4.12.6 D 4.4 4.12.9 A 6.1
6.5
4.12.1
4.12.6
C
B
6.15 4.12.9 D 6.15 4.12.9 A 6.15 4.12.6 B 2011–2012 Clark County School District Page 1 of 3 Revised: 05/25/2011 INTUITIVE GEOMETRY SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY # 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Objective Solve and prove problems using corresponding parts of congruent triangles. Solve and prove problems using corresponding parts of congruent triangles. Solve problems involving angles of a triangle.
Recognize the relationship between sides and angles of a triangle. Verify that three given sides form a triangle.
Classify polygons. Classify polygons. Solve problems involving the sum of interior angles of a given polygon. Solve problems relating to properties of quadrilaterals using algebraic techniques. Develop strategies for finding the measures of an interior angle of a given regular polygon. Explore relationships within each quadrilateral.
Distinguish among the properties of various quadrilaterals. Solve problems relating to properties of quadrilaterals using algebraic techniques. Develop strategies for finding the measures of an interior angle of a given regular polygon. Recognize the relationship between sides and angles of a triangle. Explore geometric or algebraic relationships using patterns. Compose examples of inductive and deductive reasoning. Formulate strategies for determining the slope of a line. Distinguish among the properties of various quadrilaterals. Explore relationships within each quadrilateral.
Compose examples of deductive reasoning in real‐
world situations. Distinguish between a hypothesis and the conclusion of a conditional statement. Identify parallel, perpendicular and intersecting lines using slope. Identify parallel, perpendicular and intersecting lines using slope. Propose a conclusion from given information.
Distinguish among the various terms associated with an angle. Justify conclusions to problems using the theorems related to angles. Syllabus Objective NV State Standard Key 6.14 4.12.1 B 6.14 4.12.9 C 6.5
4.12.1
A
6.2 4.12.7 D 6.3
8.1
8.1
4.12.7
4.12.1
4.12.1
B
B
D
8.3 4.12.6 C 7.3 4.12.1 B 8.2 4.12.6 A 7.2
4.12.1
D
7.1 4.12.1 C 7.3 4.12.6 B 8.2 4.12.6 B 6.2 4.12.1 A 1.5 4.12.9 C 3.7 4.12.9 B 5.2 4.12.5 B 7.1 4.12.1 A 7.2
4.12.1
A
3.6 4.12.9 C 3.1 4.12.9 A 4.1 4.12.5 C 4.1 4.12.5 D 3.5
4.12.9
D
4.6 4.12.1 A 4.11 4.12.1 A 2011–2012 Clark County School District Page 2 of 3 Revised: 05/25/2011 INTUITIVE GEOMETRY SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY # 47 48 49 50 Objective Justify conclusions to problems using the theorems related to angles. Develop accuracy using geometric tools. Distinguish among the median, altitude, angle bisector, and perpendicular bisector of a triangle. Distinguish among the median, altitude, angle bisector, and perpendicular bisector of a triangle. Syllabus Objective NV State Standard Key 4.11 4.12.1 B 2.5
3.12.3
C
6.7 4.12.1 D 6.7 4.12.1 D 2011–2012 Clark County School District Page 3 of 3 Revised: 05/25/2011