Download Unit 2 Corrective

Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry - Chapter 2 Corrective 1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Make a table of values for the rule x 2 − 16x + 64 when x is an integer from 1 to 6. Make a conjecture about
the type of number generated by the rule. Continue your table. What value of x generates a counterexample?
a. The pattern appears to be an decreasing set of perfect squares.
x = 9 generates a counterexample.
b. The pattern appears to be a decreasing set of prime numbers.
x = 8 generates a counterexample.
c. The pattern appears to be a decreasing set of perfect squares.
x = 7 generates a counterexample.
d. The pattern appears to be an increasing set of perfect squares.
x = 8 generates a counterexample.
____
2. Write the definition as a biconditional.
An acute angle is an angle whose measure is less than 90°.
a. An angle is acute if its measure is less than 90°.
b. An angle is acute if and only if its measure is less than 90°.
c. An angle’s measure is less than 90° if it is acute.
d. An angle is acute if and only if it is not obtuse.
____
3. Write a justification for each step.
m∠JKL = 100°
m∠JKL = m∠JKM + m∠MKL
100° = (6x + 8)° + (2x − 4)°
100 = 8x + 4
96 = 8x
12 = x
x = 12
a.
b.
c.
d.
[1]
Substitution Property of Equality
Simplify.
Subtraction Property of Equality
[2]
Symmetric Property of Equality
[1] Transitive Property of Equality
[2] Division Property of Equality
[1] Angle Addition Postulate
[2] Division Property of Equality
[1] Angle Addition Postulate
[2] Simplify.
[1] Segment Addition Postulate
[2] Multiplication Property of Equality
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Name: ________________________
ID: A
____
4. There is a myth that a duck’s quack does not echo. A group of scientists observed a duck in a special room,
and they found that the quack does echo. Therefore, the myth is false.
Is the conclusion a result of inductive or deductive reasoning?
a. Since the conclusion is based on a pattern of observation, it is a result of inductive
reasoning.
b. Since the conclusion is based on a pattern of observation, it is a result of deductive
reasoning.
c. Since the conclusion is based on logical reasoning from scientific research, it is a result
of inductive reasoning.
d. Since the conclusion is based on logical reasoning from scientific research, it is a result
of deductive reasoning.
____
5. Fill in the blanks to complete the two-column proof.
Given: ∠1 and ∠2 are supplementary. m∠1 = 135°
Prove: m∠2 = 45°
Proof:
Statements
1. ∠1 and ∠2 are supplementary.
2. [1]
3. m∠1 + m∠2 = 180°
4. 135° + m∠2 = 180°
5. m∠2 = 45°
a.
b.
c.
d.
Reasons
1. Given
2. Given
3. [2]
4. Substitution Property
5. [3]
[1] m∠2 = 135°
[2] Definition of supplementary angles
[3] Subtraction Property of Equality
[1] m∠1 = 135°
[2] Definition of supplementary angles
[3] Substitution Property
[1] m∠1 = 135°
[2] Definition of supplementary angles
[3] Subtraction Property of Equality
[1] m∠1 = 135°
[2] Definition of complementary angles
[3] Subtraction Property of Equality
2
Name: ________________________
ID: A
Matching
Match each vocabulary term with its definition.
a. conjecture
b. inductive reasoning
c. deductive reasoning
d. conclusion
e. biconditional statement
f. hypothesis
g. counterexample
h. conditional statement
____
6. the part of a conditional statement following the word if
____
7. the part of a conditional statement following the word then
____
8. the process of reasoning that a rule or statement is true because specific cases are true
____
9. a statement that can be written in the form “if p, then q,” where p is the hypothesis and q is the conclusion
____ 10. an example that proves that a conjecture or statement is false
____ 11. a statement that is believed to be true
Match each vocabulary term with its definition.
a. logically equivalent statements
b. deductive reasoning
c. biconditional statement
d. inductive reasoning
e. polygon
f. quadrilateral
g. pentagon
h. definition
i. triangle
____ 12. a three-sided polygon
____ 13. a closed plane figure formed by three or more segments such that each segment intersects exactly two other
segments only at their endpoints and no two segments with a common endpoint are collinear
____ 14. a statement that describes a mathematical object and can be written as a true biconditional statement
____ 15. a four-sided polygon
____ 16. a statement that can be written in the form “p if and only if q”
____ 17. the process of using logic to draw conclusions
____ 18. statements that have the same truth value
1
Name: ________________________
ID: A
Match each vocabulary term with its definition.
a. conclusion
b. converse
c. inverse
d. negation
e. hypothesis
f. truth value
g. contrapositive
____ 19. the statement formed by both exchanging and negating the hypothesis and conclusion
____ 20. the contradiction of a statement by using “not,” written as ∼
____ 21. the statement formed by exchanging the hypothesis and conclusion of a conditional statement
____ 22. operations that undo each other
____ 23. for a statement, either true (T) or false (F)
Match each vocabulary term with its definition.
a. deductive reasoning
b. paragraph proof
c. proof
d. theorem
e. inductive reasoning
f. two-column proof
g. flowchart proof
____ 24. a style of proof in which the statements are written in the left-hand column and the reasons are written in the
right-hand column
____ 25. a style of proof that uses boxes and arrows to show the structure of the proof
____ 26. a style of proof in which the statements and reasons are presented in paragraph form
____ 27. a statement that has been proven
____ 28. an argument that uses logic to show that a conclusion is true
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Name: ________________________
ID: A
Short Answer
29. Write a justification for each step, given that EG = FH .
EG = FH
EG = EF + FG
FH = FG + GH
EF + FG = FG + GH
EF = GH
Given information
[1]
Segment Addition Postulate
[2]
Subtraction Property of Equality
30. Write a conditional statement from the statement.
A horse has 4 legs.
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ID: A
Geometry - Chapter 2 Corrective 1
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
ANS:
ANS:
ANS:
ANS:
ANS:
A
B
B
A
C
TOP:
TOP:
TOP:
TOP:
TOP:
2-1 Using Inductive Reasoning to Make Conjectures
2-4 Biconditional Statements and Definitions
2-5 Algebraic Proof
2-3 Using Deductive Reasoning to Verify Conjectures
2-6 Geometric Proof
MATCHING
6.
7.
8.
9.
10.
11.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
F
D
B
H
G
A
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
2-2 Conditional Statements
2-2 Conditional Statements
2-1 Using Inductive Reasoning to Make Conjectures
2-2 Conditional Statements
2-1 Using Inductive Reasoning to Make Conjectures
2-1 Using Inductive Reasoning to Make Conjectures
12.
13.
14.
15.
16.
17.
18.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
I
E
H
F
C
B
A
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
2-4 Biconditional Statements and Definitions
2-4 Biconditional Statements and Definitions
2-4 Biconditional Statements and Definitions
2-4 Biconditional Statements and Definitions
2-4 Biconditional Statements and Definitions
2-3 Using Deductive Reasoning to Verify Conjectures
2-2 Conditional Statements
19.
20.
21.
22.
23.
ANS:
ANS:
ANS:
ANS:
ANS:
G
D
B
C
F
TOP:
TOP:
TOP:
TOP:
TOP:
2-2 Conditional Statements
2-2 Conditional Statements
2-2 Conditional Statements
2-2 Conditional Statements
2-2 Conditional Statements
24.
25.
26.
27.
28.
ANS:
ANS:
ANS:
ANS:
ANS:
F
G
B
D
C
TOP:
TOP:
TOP:
TOP:
TOP:
2-6 Geometric Proof
2-7 Flowchart and Paragraph Proofs
2-7 Flowchart and Paragraph Proofs
2-6 Geometric Proof
2-5 Algebraic Proof
1
ID: A
SHORT ANSWER
29. ANS:
[1] Segment Addition Postulate
[2] Substitution Property of Equality
TOP: 2-6 Geometric Proof
30. ANS:
If it is a horse then it has 4 legs.
TOP: 2-2 Conditional Statements
2