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Geometric Reasoning
Chapter 2 Review
Circle the best answer.
1. What is the next item in the pattern?
A
C
B
D
6. Given: Three noncollinear points lie on
the same plane. A student makes a
three-legged stool. What conclusion can
be drawn?
F The stool will wobble.
G The stool will fall over.
H The stool will not wobble.
2. Which conjecture is NOT always true?
F Intersecting lines form 4 pairs of
adjacent angles.
G Intersecting lines form 4 pairs of
linear adjacent angles.
H Intersecting lines form 4 pairs of
congruent angles.
J Not here
3. Given the conditional statement “The
counting number 0 is an integer,” what
can be concluded?
A The statement is false because the
hypothesis is false.
B The statement is false because the
conclusion is false.
C The statement is false because both
the hypothesis and the conclusion
are false.
D The statement is true.
4. Which is NOT a counterexample for the
conditional statement “If x  0, then
1
 x”?
x
1
F 2
H
2
G 1
J 2
5. Let p represent “B is between A and C”
and q represent “A, B, and C are
collinear.” Which symbolic statement
represents the conditional statement
“If B is not between A and C, then
A, B, and C are not collinear”?
A pq
C -p  -q
B qp
D
J No conclusion can be drawn.
7. If the number formed by the last two
digits of a larger number is divisible by 4,
then the larger number is divisible by 4. If
a number is divisible by 4, then it is
divisible by 2. What conclusion can be
drawn about the numbers if its last two
digits are 92?
A Only the smaller number is divisible
by 2.
B Both numbers are divisible by 2.
C Only the larger number is divisible
by 2.
D No conclusion can be drawn.
8. Which conditional statement can be used
to write a true biconditional?
F If a figure is a square, then it is a
rectangle.
G If the product is odd, then both
factors are odd.
H If two angles form a linear pair, then
they are adjacent.
J If two angles are supplementary,
then both angles are obtuse.
9. Suppose that m1  mA, and mA 
34. What can you conclude by using the
Transitive Property of Equality ?
A 34  mA
C mA  mA
B mA  m1
D m1  34
p  -q
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date ___________________ Class __________________
Chapter 2 Review continued
10. Which could NOT be used to justify
1  2?
F Trans. Prop. of 
G Reflex. Prop. of 
H Sym. Prop. of 
J Def. of 
Use the partially completed twocolumn proof for Exercises 11 and 12.
Use the two-column proof and
partially completed flowchart proof
for
Exercises 13 and 14.
Given: 1 and 2 are complementary and
1  3.
Prove: 2 and 3 are complementary.
Flowchart Proof:
Given: X is in the interior of ABC, ABC
is a right angle, and mXBC  45.
Prove: BX bisects ABC.
Proof:
Statements
Reasons
1. X is in the interior of
ABC.
1. Given
2.
2.
?
?
3. ABC is a right angle. 3. Given
4.
?
4.
?
5. mXBC  45
5. Given
6.
6. Subst.
?
7. mABX  45
7.
?
8.
8.
?
?
9. BX bisects ABC.
9. Def. of
bisector
11. Which is NOT a statement for
Steps 2, 4, 6, or 7?
A mABX  458  90
B mABC  mABX  mXBC
C mABC  90
D ABX  XBC
12. Which is NOT a reason for
Steps 2, 6, 7, or 8?
F  Add. Post.
G Subtr. Prop. of 
H Def. of rt. 
J Def. of  ?
Two-Column Proof:
Statements
Reasons
1. 1 and 2 are
complementary.
1. Given
2. m1  m2  908
2. Def. of  ?
3. 1  3
3. Given
4. m1  m3
4. Def. of 
5. m2  m3  908
5. Subst.
6. 2 and 3 are
complementary.
6. Def. of comp. ?
13. In the flowchart proof, what belongs in
the space labeled “a”?
A m3  m2  908
B 1  3
C m1  m2  908
D m1  m3
14. In the flowchart proof, what belongs in
the space labeled “b”?
F Def. of comp. ?
G Subst.
H Def. of  ?
J  Add. Post.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry