Geometry Chapter 2 Review
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
1. One way to show that a statement is NOT a good
If x = 7, then x2 = 49.
definition is to find a ____.
a. If x2 = 49, then x = 7. True; x2 = 49 if and only
a. converse
if x = 7.
b. conditional
b. If x2 = 49, then x = 7. False
c. biconditional
c. If x2 = 49, then x = 7. True; x = 7 if and only if
d. counterexample
x2 = 49.
d. If x2 = 7, then x = 49. False
2. Name the Property of Congruence that justifies the
statement:
7. What is the converse and the truth value of the
converse of the following conditional?
If
.
If an angle is a right angle, then its measure is 90.
a. Symmetric Property
a. If an angle has measure 90, then it is a right
b. Reflexive Property
angle.
c. Transitive Property
False
d. none of these
b. If an angle has measure 90, then it is a right
3. When a conditional and its converse are true, you
angle.
can combine them as a true ____.
True
a. unconditional
c. If an angle is not a right angle, then its measure
b. hypothesis
is 90.
c. biconditional
False
d. counterexample
d. If an angle is not a right angle, then its measure
is not 90.
Use the given property to complete the
True
statement.
8. Name an angle supplementary to
4. Transitive Property of Congruence
If
______.
a.
b.
c.
d.
5. Substitution Property of Equality
If
, then ______.
a.
b.
c.
d.
6. For the following true conditional statement, write
the converse. If the converse is also true, combine
the statements as a biconditional.
Fill in each missing reason.
9. Given:
Find x.
,
, and
a.
b.
c.
d.
.
P
R
Q
S
Drawing not to scale
x + 5 + x + 11 = 100
2x + 16 = 100
2x = 84
x = 42
a.
b.
c.
d.
a. _____
b. Substitution Property
c. Simplify
d. _____
e. Division Property of Equality
Protractor Postulate; Subtraction Property of Equality
Protractor Postulate; Addition Property of Equality
Angle Addition Postulate; Subtraction Property of Equality
Angle Addition Postulate; Addition Property of Equality
10. Given:
Prove:
a. Given
b. ?
c. Angle Addition Postulate
d. Substitution Property
a. Transitive Property
c. Substitution Property
b. Addition Property of Equality
d. Multiplication Property of Equality
11. Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are supplementary, then the sum of their measures is 180°.
and
are supplementary.
a.
c.
+
= 180
b.
d.
12. Which statement is the Law of Syllogism?
a. If
is a true statement and p is true, then
q is true.
+
= 90
is congruent to
b. if
c. If
.
and
are true statements, then
is a true statement.
is a true statement and q is true, then
13.
15.
16.
18.
19.
20.
p is true.
c. Billy Jones lives in Chicago, Illinois.
d. If
d. Jonah Lincoln lives in Springfield, Illinois.
and
are true statements, then
is a true statement.
14. Name the Property of Equality that justifies the
statement:
Which statement is a counterexample for the
If l = m, then
.
following conditional?
a.
Multiplication
Property
If you live in Springfield, then you live in Illinois.
b. Transitive Property
a. Erin Naismith lives in Springfield,
c. Symmetric Property
Massachusetts.
d. Subtraction Property
b. Sara Lucas lives in Springfield.
Use the Law of Syllogism to draw a conclusion from the two given statements.
If three points lie on the same line, they are collinear.
If three points are collinear, they lie in the same plane.
a. If three points do not lie in the same plane, c. The three points lie in the same plane.
they do not lie on the same line.
b. If three points lie in the same line, they lie d. The three points are collinear.
in the same plane.
If possible, use the Law of Detachment to draw a
d. not possible
conclusion from the two given statements. If not
17. Which statement is an example of the Subtraction
possible, write not possible.
Property of Equality?
Statement 1: If x = 8, then 4x – 6 = 26.
a. c = d
Statement 2: x = 8
b. If c = d then
.
a. 4x – 6 = 26
c. If c = d then
b. x = 8
d. If c = d then
c. If 4x – 6 = 26, then x = 8.
Name the Property of Congruence that justifies the statement:
If
.
a. Transitive Property
c. Reflexive Property
b. Symmetric Property
d. none of these
What is the converse of the following conditional?
If a number is a natural number, then it is a whole number.
a. If a number is a whole number, then it is a c. If a number is not a natural number, then it
natural number.
is not a whole number.
b. If a number is a natural number, then it is d. If a number is not a whole number, then it
a whole number.
is not a natural number.
Write this statement as a conditional in if-then form:
All triangles have three sides.
a. If a figure is a triangle, then it has three sides.
b. If a figure is a triangle, then all triangles have three sides.
c. If a figure has three sides, then it is not a triangle.
d. If a triangle has three sides, then all triangles have three sides.
Completion
Complete each sentence or statement.
Fill in each missing reason.
5x
4x + 3
21. Given:
Drawing not to scale
22. Write the converse of the statement. If the converse
is true, write true; if not true, provide a
counterexample.
If x = 2, then x2 = 4.
ANSWERS ON NEXT PAGE
Geometry Chapter 2 Review
Answer Section
MULTIPLE CHOICE
1.
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20.
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D
A
C
D
C
B
B
C
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B
A
B
A
C
B
A
B
A
A
A
TOP:
TOP:
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TOP:
2-4 Example 3
2-2 Example 1
2-4 Example 3
2-4 Example 3
2-2 Example 1
2-1 Example 6
2-5 Example 1
2-4 Example 1
TOP:
TOP:
TOP:
TOP:
TOP:
2-3 Example 2
2-3 Example 4
2-1 Example 3
2-4 Example 3
2-3 Example 4
TOP:
TOP:
TOP:
TOP:
2-4 Example 3
2-4 Example 3
2-1 Example 5
2-1 Example 2
COMPLETION
21. ANS:
a. Segment Addition Postulate
b. Substitution
c. Simplify
d. Subtraction Property of Equality
e. Division Property of Equality
TOP: 2-4 Example 2
22. ANS: If x2 = 4, then x = 2. False; if x2 = 4, then x can be equal to –2.
TOP: 2-1 Example 6