Download Chapter 2 Practice Test

Chapter 2 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Identify the hypothesis and conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
a. Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right
angles.
b. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are
perpendicular.
c. Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right
angles.
d. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not
perpendicular.
____
2. Write this statement as a conditional in if-then form:
All triangles have three sides.
a. If a triangle has three sides, then all triangles have three sides.
b. If a figure has three sides, then it is not a triangle.
c. If a figure is a triangle, then all triangles have three sides.
d. If a figure is a triangle, then it has three sides.
____
3. Which statement is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
a. Sara Lucas lives in Springfield.
b. Jonah Lincoln lives in Springfield, Illinois.
c. Billy Jones lives in Chicago, Illinois.
d. Erin Naismith lives in Springfield, Massachusetts.
____
4. Draw a Draw a Venn diagram to illustrate this conditional:
Cars are motor vehicles.
a.
c.
Motor vehicles
Cars
Cars
Motor vehicles
b.
d.
Motor vehicles
Cars
Cars
Motor
vehicles
____
5. Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the
____ and the part following then is the ____.
a. conditional; conclusion; hypothesis
c. conditional; hypothesis; conclusion
b. hypothesis; conclusion; conditional
d. hypothesis; conditional; conclusion
____
6. A conditional can have a ____ of true or false.
a. hypothesis
b. truth value
c. counterexample
d. conclusion
____
7. Which choice shows a true conditional with the hypothesis and conclusion identified correctly?
a. Yesterday was Monday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Monday.
b. If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is not Thursday.
c. If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is Thursday.
d. Yesterday was Tuesday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Tuesday.
____
8. What is the conclusion of the following conditional?
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
a. The number is odd.
b. The sum of the digits of the number is divisible by 3.
c. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
d. The number is divisible by 3.
____
9. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
a. If a point is in the first quadrant, then its coordinates are positive.
b. If a point is not in the first quadrant, then the coordinates of the point are not positive.
c. If the coordinates of a point are positive, then the point is in the first quadrant.
d. If the coordinates of a point are not positive, then the point is not in the first quadrant.
____ 10. What is the converse and the truth value of the converse of the following conditional?
If an angle is a right angle, then its measure is 90.
a. If an angle is not a right angle, then its measure is 90.
False
b. If an angle is not a right angle, then its measure is not 90.
True
c. If an angle has measure 90, then it is a right angle.
False
d. If an angle has measure 90, then it is a right angle.
True
____ 11. For the following true conditional statement, write the converse. If the converse is also true, combine the
statements as a biconditional.
If x = 3, then x2 = 9.
a. If x2 = 9, then x = 3. True; x2 = 9 if and only if x = 3.
b. If x2 = 3, then x = 9. False
c. If x2 = 9, then x = 3. True; x = 3 if and only if x2 = 9.
d. If x2 = 9, then x = 3. False
____ 12. Determine whether the conditional and its converse are both true. If both are true, combine them as a
biconditional. If either is false, give a counterexample.
If two lines are parallel, they do not intersect.
If two lines do not intersect, they are parallel.
a. One statement is false. If two lines do not intersect, they could be skew..
b. One statement is false. If two lines are parallel, they may intersect twice.
c. Both statements are true. Two lines are parallel if and only if they do not intersect.
d. Both statements are true. Two lines are not parallel if and only if they do not intersect.
____ 13. Determine whether the conditional and its converse are both true. If both are true, combine them as a
biconditional. If either is false, give a counterexample.
If an angle is a right angle, its measure is 90.
If an angle measure is 90, the angle is a right angle.
a. One statement is false. If an angle measure is 90, the angle may be a vertical angle.
b. One statement is false. If an angle is a right angle, its measure may be 180.
c. Both statements are true. An angle is a right angle if and only if its measure is 90.
d. Both statements are true. The measure of angle is 90 if and only if it is not a right angle.
____ 14. When a conditional and its converse are true, you can combine them as a true ____.
a. counterexample
c. unconditional
b. biconditional
d. hypothesis
____ 15. Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a true
biconditional.
Two lines that intersect at right angles are perpendicular.
a. The statement is not reversible.
b. Reversible; if two lines intersect at right angles, then they are perpendicular.
c. Reversible; if two lines are perpendicular, then they intersect at right angles.
d. Reversible; two lines intersect at right angles if and only if they are perpendicular.
____ 16. Is the statement a good definition? If not, find a counterexample.
A square is a figure with two pairs of parallel sides and four right angles.
a. The statement is a good definition.
b. No; a rhombus is a counterexample.
c. No; a rectangle is a counterexample.
d. No; a parallelogram is a counterexample.
____ 17. One way to show that a statement is NOT a good definition is to find a ____.
a. converse
c. biconditional
b. conditional
d. counterexample
____ 18. Which statement provides a counterexample to the following faulty definition?
A square is a figure with four congruent sides.
a. A six-sided figure can have four sides congruent.
b. Some triangles have all sides congruent.
c. A square has four congruent angles.
d. A rectangle has four sides.
____ 19. Which biconditional is NOT a good definition?
a. A whole number is odd if and only if the number is not divisible by 2.
b. An angle is straight if and only if its measure is 180.
c. A whole number is even if and only if it is divisible by 2.
d. A ray is a bisector of an angle if and only if it splits the angle into two angles.
Fill in each missing reason.
____ 20. Given:
Find x.
,
P
, and
.
R
Q
S
Drawing not to scale
x – 5 + x – 11 = 100
2x – 16 = 100
2x = 116
x = 58
a.
b.
c.
d.
a. _____
b. Substitution Property
c. Simplify
d. _____
e. Division Property of Equality
Angle Addition Postulate; Subtraction Property of Equality
Protractor Postulate; Addition Property of Equality
Angle Addition Postulate; Addition Property of Equality
Protractor Postulate; Subtraction Property of Equality
____ 21. Given:
Prove:
a. a. Given
b. Symmetric Property of Equality
c. Subtraction Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
b. a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Division Property of Equality
e. Symmetric Property of Equality
c. a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
d. a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Addition Property of Equality
e. Symmetric Property of Equality
____ 22. Name the Property of Equality that justifies the statement:
If p = q, then
.
a. Reflexive Property
c. Symmetric Property
b. Multiplication Property
d. Subtraction Property
____ 23. Which statement is an example of the Addition Property of Equality?
a. If p = q then
c. If p = q then
b. If p = q then
d. p = q
.
____ 24. Name the Property of Congruence that justifies the statement:
If
.
a. Symmetric Property
c. Reflexive Property
b. Transitive Property
d. none of these
____ 25. Name the Property of Congruence that justifies the statement:
If
.
a. Transitive Property
c. Reflexive Property
b. Symmetric Property
d. none of these
Use the given property to complete the statement.
____ 26. Transitive Property of Congruence
If
______.
a.
b.
c.
d.
____ 27. Multiplication Property of Equality
If
, then ______.
a.
b.
c.
d.
____ 28. Substitution Property of Equality
If
, then ______.
a.
b.
____ 29.
bisects
a. 50
= 7x.
b. 125
c.
d.
=
. Find
c. 75
d. 175
c. 19
d. 55
c. 27
d. 153
____ 30. Find the value of x.
(7x – 8)°
(6x + 11)°
Drawing not to scale
a. –19
____ 31.
b. 125
Find
1
4
2
3
Drawing not to scale
a. 37
b. 143
____ 32. Find the values of x and y.
4y°
112°
7x + 7°
Drawing not to scale
a. x = 15, y = 17
c. x = 68, y = 112
b. x = 112, y = 68
d. x = 17, y = 15
Short Answer
33. Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16.
34. Write the converse of the given true conditional and decide whether the converse is true or false. If the
converse is true, combine it with the conditional to form a true biconditional. If the converse is false, give a
counterexample.
If the probability that an event will occur is 0, then the event is impossible to occur.
Fill in each missing reason.
35. Given:
(2x)°
6(x – 3)°
Drawing not to scale
36. Given:
2x
6x + 8
Drawing not to scale
37. Complete the paragraph proof.
Given:
are supplementary, and
are supplementary.
Prove:
By the definition of supplementary angles,
by _____ (c). Subtract
_____ (e).
_____ (a) and
from each side. You get
38. Solve for x. Justify each step.
39. Write the conditional statement that the Venn diagram illustrates.
Quadrilaterals
Squares
Essay
40. Given:
Prove:
are complementary, and
are complementary.
_____ (b). Then
_____ (d), or
Fill in each missing reason.
41. Given:
Prove:
Drawing not to scale
Other
42. a. Write the following conditional in if-then form.
b. Write its converse in if-then form.
c. Determine the truth value of the original conditional and its converse. Explain why each of them is true or
false, and provide a counterexample(s) for any false statement(s).
On a number line, the points with coordinates –2 and 5 are 7 units apart.
43. Write the two conditional statements that form the given biconditional. Then decide whether the biconditional
is a good definition. Explain.
Three points are collinear if and only if they are coplanar.
44. Give a convincing argument that the following statement is true.
If two angles are congruent and complementary, then the measure of each is 45.
Chapter 2 Practice Test
Answer Section
MULTIPLE CHOICE
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B
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.1 Conditional Statements
TOP: 2-1 Example 1
conditional statement | hypothesis | conclusion
D
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.1 Conditional Statements
TOP: 2-1 Example 2
hypothesis | conclusion | conditional statement
D
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.1 Conditional Statements
TOP: 2-1 Example 3
conditional statement | counterexample
A
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.1 Conditional Statements
TOP: 2-1 Example 4
conditional statement | Venn Diagram
C
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.1 Conditional Statements
TOP: 2-1 Example 1
conditional statement | hypothesis | conclusion
B
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.1 Conditional Statements
TOP: 2-1 Example 3
conditional statement | truth value
D
PTS: 1
DIF: L3
REF: 2-1 Conditional Statements
2-1.1 Conditional Statements
conditional statement | truth value | hypothesis | conclusion
D
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.1 Conditional Statements
TOP: 2-1 Example 1
conditional statement | conclusion
C
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.2 Converses
TOP: 2-1 Example 5
conditional statement | coverse of a conditional
D
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
2-1.2 Converses
TOP: 2-1 Example 6
conditional statement | coverse of a conditional | truth value
D
PTS: 1
DIF: L2
REF: 2-2 Biconditionals and Definitions
2-2.1 Writing Biconditionals
TOP: 2-2 Example 1
conditional statement | coverse of a conditional | biconditional statement
A
PTS: 1
DIF: L2
REF: 2-2 Biconditionals and Definitions
2-2.1 Writing Biconditionals
TOP: 2-2 Example 1
conditional statement | coverse of a conditional | biconditional statement | counterexample
C
PTS: 1
DIF: L2
REF: 2-2 Biconditionals and Definitions
2-2.1 Writing Biconditionals
TOP: 2-2 Example 1
conditional statement | coverse of a conditional | biconditional statement | counterexample
B
PTS: 1
DIF: L2
REF: 2-2 Biconditionals and Definitions
2-2.1 Writing Biconditionals
TOP: 2-2 Example 1
conditional statement | biconditional statement
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D
PTS: 1
DIF: L2
REF: 2-2 Biconditionals and Definitions
2-2.2 Recognizing Good Definitions
TOP: 2-2 Example 3
biconditional statement
C
PTS: 1
DIF: L2
REF: 2-2 Biconditionals and Definitions
2-2.2 Recognizing Good Definitions
TOP: 2-2 Example 4
biconditional statement | counterexample
D
PTS: 1
DIF: L2
REF: 2-2 Biconditionals and Definitions
2-2.2 Recognizing Good Definitions
KEY: counterexample
A
PTS: 1
DIF: L3
REF: 2-2 Biconditionals and Definitions
2-2.2 Recognizing Good Definitions
KEY: counterexample
D
PTS: 1
DIF: L3
REF: 2-2 Biconditionals and Definitions
2-2.2 Recognizing Good Definitions
KEY: biconditional statement
C
PTS: 1
DIF: L2
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
2-4 Example 1
Properties of Equality | Angle Addition Postulate | deductive reasoning
B
PTS: 1
DIF: L3
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
Properties of Equality | proof
D
PTS: 1
DIF: L2
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
2-4 Example 3
KEY: Properties of Equality
B
PTS: 1
DIF: L2
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
2-4 Example 3
KEY: Properties of Equality
A
PTS: 1
DIF: L2
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
2-4 Example 3
KEY: Properties of Congruence
A
PTS: 1
DIF: L2
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
2-4 Example 3
KEY: Properties of Congruence
C
PTS: 1
DIF: L3
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
2-4 Example 3
KEY: Properties of Congruence
C
PTS: 1
DIF: L3
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
2-4 Example 3
KEY: Properties of Equality
C
PTS: 1
DIF: L3
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
2-4 Example 3
KEY: Properties of Equality
D
PTS: 1
DIF: L4
REF: 2-4 Reasoning in Algebra
2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
Properties of Congruence | Properties of Equality | deductive reasoning
C
PTS: 1
DIF: L2
REF: 2-5 Proving Angles Congruent
2-5.1 Theorems About Angles
STA: CA GEOM 1.0| CA GEOM 2.0| CA GEOM 4.0
2-5 Example 1
KEY: vertical angles | Vertical Angles Theorem
A
PTS: 1
DIF: L2
REF: 2-5 Proving Angles Congruent
2-5.1 Theorems About Angles
STA: CA GEOM 1.0| CA GEOM 2.0| CA GEOM 4.0
2-5 Example 1
KEY: Vertical Angles Theorem | vertical angles
32. ANS:
OBJ:
TOP:
KEY:
A
PTS: 1
DIF: L2
REF: 2-5 Proving Angles Congruent
2-5.1 Theorems About Angles
STA: CA GEOM 1.0| CA GEOM 2.0| CA GEOM 4.0
2-5 Example 1
Vertical Angles Theorem | vertical angles | supplementary angles | multi-part question
SHORT ANSWER
33. ANS:
If x2 = 16, then x = 4. False; if x2 = 16, then x can be equal to –4.
PTS: 1
DIF: L2
REF: 2-1 Conditional Statements
OBJ: 2-1.2 Converses
TOP: 2-1 Example 6
KEY: conditional statement | coverse of a conditional | counterexample | truth value
34. ANS:
If an event is impossible, the probability of the event is 0.
True
An event is impossible if and only if the probability of the event is zero.
PTS: 1
DIF: L2
REF: 2-2 Biconditionals and Definitions
OBJ: 2-2.1 Writing Biconditionals
TOP: 2-2 Example 1
KEY: conditional statement | coverse of a conditional | counterexample | biconditional statement | truth value
| multi-part question
35. ANS:
a. Angle Addition Postulate
b. Substitution Property
c. Distributive Property
d. Simplify
e. Addition Property of Equality
f. Division Property of Equality
PTS: 1
DIF: L3
REF: 2-4 Reasoning in Algebra
OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
TOP: 2-4 Example 1
KEY: proof | deductive reasoning | Properties of Equality | multi-part question
36. ANS:
a. Segment Addition Postulate
b. Substitution
c. Simplify
d. Subtraction Property of Equality
e. Division Property of Equality
PTS: 1
DIF: L3
REF: 2-4 Reasoning in Algebra
OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
TOP: 2-4 Example 2
KEY: deductive reasoning | proof | Properties of Equality
37. ANS:
a. 180
b. 180
c. Transitive Property (or Substitution Property)
d.
e.
PTS:
OBJ:
TOP:
KEY:
38. ANS:
1
DIF: L2
REF: 2-5 Proving Angles Congruent
2-5.1 Theorems About Angles
STA: CA GEOM 1.0| CA GEOM 2.0| CA GEOM 4.0
2-5 Example 2
Properties of Equality | deductive reasoning | proof | supplementary angles
Given
Addition Property of Equality
Simplify
Division Property of Equality
x = 27
Simplify
PTS: 1
DIF: L4
REF: 2-4 Reasoning in Algebra
OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry
STA: CA GEOM 1.0| CA GEOM 3.0
KEY: Properties of Equality | proof | deductive reasoning
39. ANS:
If a figure is a square, then it is a quadrilateral.
PTS: 1
DIF: L3
REF: 2-1 Conditional Statements
OBJ: 2-1.1 Conditional Statements
TOP: 2-1 Example 4
KEY: Venn Diagram | conditional statement
ESSAY
40. ANS:
[4] By the definition of complementary angles,
and
By the Transitive Property of Equality (or Substitution Property),
. By the Subtraction Property of Equality,
by the definition of congruent angles.
OR
equivalent explanation
[3] one step missing OR one incorrect justification
[2] two steps missing OR two incorrect justifications
[1] correct steps with no explanations
.
, and
PTS: 1
DIF: L4
REF: 2-5 Proving Angles Congruent
OBJ: 2-5.1 Theorems About Angles
STA: CA GEOM 1.0| CA GEOM 2.0| CA GEOM 4.0
KEY: complementary angles | Properties of Equality | rubric-based question | extended response | proof
41. ANS:
[4] a. Given
b. Substitution Property
c. Vertical Angles Theorem
d. Substitution Property
[3] three parts correct
[2] two parts correct
[1] one part correct
PTS: 1
DIF: L4
REF: 2-5 Proving Angles Congruent
OBJ: 2-5.1 Theorems About Angles
STA: CA GEOM 1.0| CA GEOM 2.0| CA GEOM 4.0
KEY: Vertical Angles Theorem | proof | extended response | rubric-based question
OTHER
42. ANS:
a. On a number line, if points have coordinates –2 and 5, then they are 7 units apart.
b. On a number line, if points are 7 units apart, then they have coordinates –2 and 5.
c. The original conditional is true by the Ruler Postulate. The converse is false. The points 0 and 7 and 7 units
apart, but their coordinates are not –2 and 5.
PTS: 1
DIF: L3
REF: 2-1 Conditional Statements
OBJ: 2-1.2 Converses
TOP: 2-1 Example 7
KEY: multi-part question | writing in math | conditional statement | coverse of a conditional | truth value
43. ANS:
If three points are collinear, then they are coplanar.
If three points are coplanar, then they are collinear.
The biconditional is not a good definition.
Three coplanar points might not lie on the same line.
PTS: 1
DIF: L3
REF: 2-2 Biconditionals and Definitions
OBJ: 2-2.2 Recognizing Good Definitions
KEY: writing in math | biconditional statement | multi-part question
44. ANS:
Explanations may vary. Sample: If two angles are congruent and complementary, they have equal measures
that add to 90. Thus, each angle has a measure that is one-half of 90, or 45.
PTS: 1
DIF: L3
REF: 2-5 Proving Angles Congruent
OBJ: 2-5.1 Theorems About Angles
STA: CA GEOM 1.0| CA GEOM 2.0| CA GEOM 4.0
KEY: writing in math | complementary angles