GEOM CH. 2 REVIEW
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1. What is the conclusion of the following
conditional?
A number is divisible by 2 if the number is even.
A. The sum of the digits of the number is
divisible by 2.
B. If a number is even, then the number is
divisible by 2.
C. The number is even.
D. The number is divisible by 2.
____
2. 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.
3. 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.
____
4. 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;
C. conditional;
conclusion;
hypothesis;
hypothesis
conclusion
B. hypothesis;
D. hypothesis;
conclusion;
conditional;
conditional
conclusion
5. 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.
6. 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
7. A conditional can have a ____ of true or false.
A. hypothesis
C. counterexample
B. truth value
D. conclusion
8.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.
____ 9. What is the converse of the following conditional?
If a point is in the fourth quadrant, then its
____
coordinates are negative.
A. If a point is in the fourth quadrant, then its
coordinates are negative.
B. If a point is not in the fourth quadrant, then
the coordinates of the point are not negative.
C. If the coordinates of a point are not negative,
then the point is not in the fourth quadrant.
D. If the coordinates of a point are negative,
then the point is in the fourth quadrant.
____ 10. Which conditional has the same truth value as its
converse?
A. If x = 7, then
.
B. If a figure is a square, then it has four sides.
C. If x – 17 = 4, then x = 21.
D. If an angle has a measure of 80, then it is
acute.
____
____ 11. For the following true conditional statement, write
the converse. If the converse is also true, combine
the statements as a biconditional.
If x = 7, then x2 = 49.
A. If x2 = 49, then x = 7. True; x2 = 49 if and
only if x = 7.
B. If x2 = 49, then x = 7. True; x = 7 if and only
if x2 = 49.
C. If x2 = 49, then x = 7. False
D. If x2 = 7, then x = 49. False
____ 12. What is the converse of the following true
conditional? If the converse is true, rewrite the
statements as a biconditional. If either is false, ____
give a counterexample.
If two lines are parallel, they do not intersect.
A. If two lines do not intersect, they are
parallel. One statement is false. If two lines
do not intersect, they could be skew.
B. If two lines do not intersect, they are
parallel. One statement is false. If two lines
are parallel, they may intersect twice.
C. If two lines do not intersect, they are
parallel. Both statements are true. Two lines ____
are parallel if (and only if) they do not
13.
14.
15.
16.
intersect.
D. If two lines do not intersect, they are not
parallel. Both statements are true. Two lines
are not parallel if (and only if) they do not
intersect.
When a conditional and its converse are true,
you can combine them as a true ____.
A. counterexample
C. unconditional
B. biconditional
D. hypothesis
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.
Write the two conditional statements that make
up the following biconditional.
I drink juice if (and only if) it is breakfast time.
A. I drink juice if (and only if) it is breakfast
time.
It is breakfast time if (and only if) I drink
juice.
B. If I drink juice, then it is breakfast time.
If it is breakfast time, then I drink juice.
C. If I drink juice, then it is breakfast time.
I drink juice only if it is breakfast time.
D. I drink juice.
It is breakfast time.
Is the following definition of dog reversible? If
yes, write it as a true biconditional.
A dog is a mammal.
A. The reverse is false.
B. The reverse is true. An animal is a dog if
(and only if) it is a mammal.
C. The reverse is true. An animal is a mammal
if (and only if) it is a dog.
D. The reverse is true. If an animal is a dog,
then it is a mammal.
17.Is the following definition of perpendicular reversible? If
yes, write it as a true biconditional.
P
R
Two lines that intersect at right angles are
perpendicular.
A. The statement is not reversible.
B. Yes; if two lines intersect at right angles,
then they are perpendicular.
Q
S
C. Yes; if two lines are perpendicular, then they
Drawing not to scale
intersect at right angles.
D. Yes; two lines intersect at right angles if
(and only if) they are perpendicular.
a.
____ 18. Is the statement a good definition? If not, find a
__________
counterexample.
b.
A square is a figure with two pairs of parallel sides
x – 5 + x – 7 = 100
Substitution
and four right angles.
Property
A. The statement is a good definition.
2x – 12 = 100
c. Simplify
B. No; a rhombus is a counterexample.
d.
2x = 112
C. No; a rectangle is a counterexample.
__________
D. No; a parallelogram is a counterexample.
e. Division
x = 56
Property of
____ 19. One way to show that a statement is NOT a good
Equality
definition is to find a ____.
A. converse
C. biconditional
A. Angle Addition Postulate; Subtraction
B. conditional
D. counterexample
Property of Equality
____ 20. Which statement provides a counterexample to the
B. Angle Addition Postulate; Addition Property
following faulty definition?
of Equality
A square is a figure with four congruent sides.
C.
Protractor Postulate; Addition Property of
A. A six-sided figure can have four sides
Equality
congruent.
D.
Protractor Postulate; Subtraction Property of
B. Some triangles have all sides congruent.
Equality
C. A square has four congruent angles.
D. A rectangle has four sides.
____ 23.
bisects
= 7x.
=
. Find
____ 21. Which biconditional is NOT a good definition?
A. 108
B. 72
C. 180
D. 252
A. A whole number is even if and only if it is
divisible by 2.
____ 24. Name the Property of Equality that justifies this
B. A whole number is odd if and only if the
statement:
number is not divisible by 2.
If l = m, then
.
C. An angle is straight if and only if its measure
A. Multiplication
C. Subtraction
is 180.
Property
Property
D. A ray is a bisector of an angle if and only if
B. Symmetric Property D. Transitive
it splits the angle into two angles.
Property
____ 22. What is the value of x? Identify the missing
____ 25. Which statement is an example of the Addition
justifications.
Property of Equality?
,
, and
A. If p = q then
C. If p = q then
.
.
.
B. If p = q then
D. p = q
.
Use the given property to complete the
statement.
____ 26. Transitive Property of Congruence
If
______.
A.
C.
B.
D.
(8x – 8)°
(7x + 8)°
____ 27. Multiplication Property of Equality
If
, then ______.
Drawing not to scale
A.
C.
B.
D.
A. –16
B. 120
C. 60
____ 28. Substitution Property of Equality
____ 34. What is the value of x?
If
, then ______.
A.
C.
B.
D.
(2x + 24)º
____ 29. Name the Property of Congruence that justifies the
statement:
144 º
If
.
A. Symmetric Property C. Reflexive Property
Drawing not to scale
B. Transitive Property D. none of these
____ 30. Name the Property of Congruence that justifies
this statement:
A. 84
B. 36
C. 120
If
.
Find
A. Transitive Property C. Reflexive Property ____ 35.
B. Symmetric Property D. none of these
____ 31. Complete the two-column proof.
D. 16
D. 60
1
Given:
4
2
3
Prove:
Drawing not to scale
A. 150
____
33.What is the value of x?
B. 30
C. 160
D. 20
36.Find the values of x and y.
measure is not 90.
True
C. If an angle has a measure of 90, then it is a
right angle.
False
D. If an angle has a measure of 90, then it is a
right angle.
True
41. 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.
A. x = 15, y = 17
C. x = 68, y = 112
B. x = 112, y = 68
D. x = 17, y = 15
37. Write the conditional statement that the Venn
diagram illustrates.
Quadrilaterals
Squares
38. Is the following conditional true or false? If it is
true, explain why. If it is false, give a
counterexample.
If it is snowing in Dallas, Texas, then it is snowing
in the United States.
39. 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.
____ 40. 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
42. For the given statements below, write the first
statement as a conditional in if-then form. Then,
if possible, use the Law of Detachment to draw a
conclusion from the two given statements. If not
possible, write not possible. Explain.
A straight angle has a measure of 180.
is a straight angle.
43. A plumber knows that if you shut off the water
at the main valve, it is safe to remove the sink
faucet. The plumber turns the main valve to the
“off” position. What conclusion can the plumber
make?
44. Use the Law of Detachment to draw a
conclusion from the two given statements. If not
possible, state not possible. Explain.
Statement 1: If two lines intersect, then they are
not parallel.
Statement 2:
do not intersect.
45.What is the value of x? Identify the missing justifications.
Given:
are supplementary, and
are supplementary.
Prove:
By the definition of supplementary angles,
_____ (a) and
_____ (b). Then
by _____ (c).
Subtract
from each side. You get
_____ (d), or
_____ (e).
46. Solve for x. Justify each step.
47. What is the value of x? Justify each step.
48. Complete the paragraph proof.
Answer Section
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36.
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D
B
D
C
D
A
B
D
D
C
C
A
B
C
B
A
D
C
D
A
D
B
D
B
B
D
A
B
A
A
B
D
D
B
A
37. ANS:
If a figure is a square, then it is a quadrilateral.
38. ANS:
True. Dallas, Texas is a city that lies within the
United States.
39. ANS:
If x2 = 16, then x = 4. False; if x2 = 16, then x can
be equal to –4.
40.
ANS: D
41. ANS:
42.
43.
44.
45.
46.
47.
48.
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.
ANS:
If an angle is straight, then its measure is 180.
Conclusion:
is 180.
ANS:
It is safe to remove the sink faucet.
ANS:
Not possible. Explanations may vary. Sample:
To use the Law of Detachment, you must know
that the hypothesis is true.
ANS:
a. Angle Addition Postulate
b. Substitution Property
c. Distributive Property
d. Simplify
e. Addition Property of Equality
f. Division Property of Equality
ANS:
Given
Addition Property of
Equality
Simplify
Division Property of
Equality
x = 27
Simplify
ANS:
a. Segment Addition Postulate
b. Substitution
c. Simplify
d. Subtraction Property of Equality
e. Division Property of Equality
ANS:
a. 180
b. 180
c. Transitive Property (or Substitution Property)
d.
e.