Download Geometric Reasoning

Name ________________________________________ Date ___________________ Class __________________
Chapter
2
Geometric Reasoning
Chapter Test Form B
Circle the best answer.
6. Given: If one angle of a triangle is a right
angle, then the other two angles are both
acute. A triangle has a 45� angle.
What conclusion can be drawn?
1. What is the next item in the pattern?
−1, 2, −4, 8, . . .
A −16
C 4
B −4
D 16
F One of the other two angles is 90°.
G One of the other two angles is obtuse.
2. Which is a counterexample that shows
that the following conjecture is false: “If
∠1 and ∠2 are supplementary, then one
of the angles is obtuse”?
H All three angles are acute.
J No conclusion can be drawn.
7. Which symbolic statement represents the
Law of Syllogism?
F m∠1 = 45° and m∠2 = 45°
G m∠1 = 53° and m∠2 = 127°
A If p → q and q → r are true statements,
then p → r is a true statement.
H m∠1 = 90° and m∠2 = 90°
B If p → q and p → r are true statements,
then q → r is a true statement.
J m∠1 = 100° and m∠2 = 80°
3. Given: All snarfs are yelbs. All yelbs are
blue. Migs can be either green or pink.
Some slokes are snarfs. What conclusion
can be drawn?
C If p → q and r → q are true statements,
then q → p is a true statement.
D If p → r and q → r are true statements,
then p → q is a true statement.
A Some migs are snarfs.
8. Which is a biconditional statement of the
conditional statement “If x3 = −1, then
x = −1”?
B Some snarfs are green.
C Some slokes are yelbs.
D All slokes are migs.
F If x = −1, then x3 = −1.
4. Given the conditional statement “If it is
January, then it is winter in the United
States,” which is true?
G x3 = −1 if x = −1.
H x3 = −1 if and only if x = −1.
J x = −1 → x3 = −1.
F the converse of the conditional
G the inverse of the conditional
9. Which property is NOT used when
solving 15 = 2x − 1?
H the contrapositive of the conditional
A Reflex. Prop. of =
J Not here
B Add. Prop. of =
5. What is the inverse of the conditional
statement “If a number is divisible by 6,
then it is divisible by 3”?
C Div. Prop. of =
D Sym. Prop. of =
A If a number is divisible by 3, then it is
divisible by 6.
10. Identify the property that justifies the
statement “If ∠B ≅ ∠A, then
∠A ≅ ∠B.”
B If a number is not divisible by 6, then
it is not divisible by 3.
F Sym. Prop. of =
C If a number is not divisible by 3, then
it is not divisible by 6.
G Reflex. Prop. of =
D If a number is not divisible by 6, then
it is divisible by 3.
J Sym. Prop. of ≅
H Trans. Prop. of ≅
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
29
Holt McDougal Geometry
Name ________________________________________ Date ___________________ Class __________________
Chapter
2
Geometric Reasoning
Chapter Test Form B continued
Use the partially completed two-column
proof for Exercises 11 and 12.
Use the partially completed two-column
and flowchart proofs for Exercises 13
and 14.
Given: m∠1 = 30� and m∠2 = 2m∠1.
Prove: ∠1 and ∠2 are complementary.
Proof:
Statements
Given: ∠2 ≅ ∠3, and ∠1 and ∠2 are adjacent
angles whose noncommon sides form
a straight line.
Prove: ∠1 and ∠3 are supplementary.
Two-Column Proof:
Reasons
1. m∠1 = 30°,
m∠2 = 2m∠1
1. Given
2.
?
2.
?
1. ∠2 ≅ ∠3
1. Given
3.
?
3.
?
2. m∠2 = m∠3
2. Def. of ≅ �
4.
?
4.
?
3.
5.
?
5. Simplify.
3. ∠1 and ∠2 are
supplementary.
4. m∠1 + m∠2 = 180°
4. Def. of supp. �
5. m∠1 + m∠3 = 180°
5.
6. ∠1 and ∠3 are
supplementary.
6. Def. of supp. �
6. ∠1 and ∠2 are
complementary.
Statements
6. Def. of comp. �
11. Each of the items listed below belongs in
one of the blanks in the Statements
column. Which belongs in Step 4?
Reasons
?
?
Flowchart Proof:
A m∠2 = 2(30°)
B m∠1 + m∠2 = 90°
C m∠1 + m∠2 = 30° + 60°
D m∠2 = 60°
12. Which is the justification for Step 2?
F Add. Prop. of =
13. In the flowchart proof, which belongs in
the last blank box?
G Simplify.
H Subst.
A m∠1 + m∠2 = 180°
J ∠ Add. Post.
B Def. of supp. �
C m∠1 + m∠3 = 180°
D Subst.
14. In the flowchart proof, which theorem
justifies the statement “∠1 and ∠2 are
supplementary”?
F Linear Pair Theorem
G Congruent Supplements Theorem
H Right Angle Congruence Theorem
J Congruent Complements Theorem
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
30
Holt McDougal Geometry