Download Unit 2 Review

Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry - Chapter 2 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine if the conjecture is valid by the Law of Syllogism.
Given: If you are in California, then you are in the west coast. If you are in Los Angeles, then you are in
California.
Conjecture: If you are in Los Angeles, then you are in the west coast.
a. No, the conjecture is not valid.
b. Yes, the conjecture is valid.
____
2. Use the Law of Syllogism to draw a conclusion from the given information.
Given: If two lines are perpendicular, then they form right angles. If two lines meet at a 90° angle, then they
are perpendicular. Two lines meet at a 90° angle.
a. Conclusion: The lines are parallel.
b. Conclusion: The lines are perpendicular and meet at a 90° angle.
c. Conclusion: The lines meet at a 90° angle.
d. Conclusion: The lines form a right angle.
____
3. For the conditional statement, write the converse and a biconditional statement.
If a figure is a right triangle with sides a, b, and c, then a 2 + b 2 = c 2 .
a. Converse: If a figure is not a right triangle with sides a, b, and c, then a 2 + b 2 ≠ c 2 .
Biconditional: A figure is a right triangle with sides a, b, and c if and only if
a2 + b2 = c2.
b. Converse: If a 2 + b 2 = c 2 , then the figure is a right triangle with sides a, b, and c.
Biconditional: A figure is a right triangle with sides a, b, and c if and only if
a2 + b2 = c2.
c. Converse: If a 2 + b 2 ≠ c 2 , then the figure is not a right triangle with sides a, b, and c.
Biconditional: A figure is not a right triangle with sides a, b, and c if and only if
a2 + b2 ≠ c2
d. Converse: If a 2 + b 2 ≠ c 2 , then the figure is not a right triangle with sides a, b, and c.
Biconditional: A figure is a right triangle with sides a, b, and c if and only if
a2 + b2 = c2.
____
4. Determine if the biconditional is true. If false, give a counterexample.
A figure is a square if and only if it is a rectangle.
a. The biconditional is true.
b. The biconditional is false. A rectangle does not necessarily have four congruent sides.
c. The biconditional is false. All squares are parallelograms with four 90° angles.
d. The biconditional is false. A rectangle does not necessarily have four 90° angles.
1
Name: ________________________
ID: A
____
5. 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.
____
6. Solve the equation 4x − 6 = 34. Write a justification for each step.
4x − 6 = 34
Given equation
[1]
+6 +6
4x
= 40
Simplify.
4x
40
=
[2]
4
4
x = 10
Simplify.
a.
b.
[1] Substitution Property of Equality;
[2] Division Property of Equality
[1] Addition Property of Equality;
[2] Division Property of Equality
c.
d.
[1] Division Property of Equality;
[2] Subtraction Property of Equality
[1] Addition Property of Equality;
[2] Reflexive Property of Equality
Short Answer
7. Find the next item in the pattern 2, 3, 5, 7, 11, ...
8. How many true conditional statements may be written using the following statements?
n is a rational number.
n is an integer.
n is a whole number.
9. Write the conditional statement and converse within the biconditional.
A rectangle is a square if and only if all four sides of the rectangle have equal lengths.
10. Identify the property that justifies the statement.
AB ≅ CD and CD ≅ EF . So AB ≅ EF .
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
____ 11. an example that proves that a conjecture or statement is false
____ 12. a statement that is believed to be true
____ 13. the part of a conditional statement following the word then
____ 14. the part of a conditional statement following the word if
____ 15. the process of reasoning that a rule or statement is true because specific cases are true
____ 16. a statement that can be written in the form “if p, then q,” where p is the hypothesis and q is the conclusion
Match each vocabulary term with its definition.
a. conclusion
b. converse
c. inverse
d. negation
e. hypothesis
f. truth value
g. contrapositive
____ 17. for a statement, either true (T) or false (F)
____ 18. operations that undo each other
____ 19. the contradiction of a statement by using “not,” written as ∼
____ 20. the statement formed by exchanging the hypothesis and conclusion of a conditional statement
____ 21. the statement formed by both exchanging and negating the hypothesis and conclusion
1
Name: ________________________
ID: A
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
____ 22. a statement that describes a mathematical object and can be written as a true biconditional statement
____ 23. statements that have the same truth value
____ 24. a four-sided polygon
____ 25. 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
____ 26. the process of using logic to draw conclusions
____ 27. a statement that can be written in the form “p if and only if q”
____ 28. a three-sided polygon
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
____ 29. 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
____ 30. a statement that has been proven
____ 31. a style of proof in which the statements and reasons are presented in paragraph form
____ 32. an argument that uses logic to show that a conclusion is true
____ 33. a style of proof that uses boxes and arrows to show the structure of the proof
4
ID: A
Geometry - Chapter 2 Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
D
B
B
B
B
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
2-3 Using Deductive Reasoning to Verify Conjectures
2-3 Using Deductive Reasoning to Verify Conjectures
2-4 Biconditional Statements and Definitions
2-4 Biconditional Statements and Definitions
2-4 Biconditional Statements and Definitions
2-5 Algebraic Proof
SHORT ANSWER
7. ANS:
13
TOP: 2-1 Using Inductive Reasoning to Make Conjectures
8. ANS:
3 conditional statements
TOP: 2-2 Conditional Statements
9. ANS:
Conditional: If all four sides of the rectangle have equal lengths, then it is a square.
Converse: If a rectangle is a square, then its four sides have equal lengths.
TOP: 2-4 Biconditional Statements and Definitions
10. ANS:
Transitive Property of Congruence
TOP: 2-5 Algebraic Proof
MATCHING
11.
12.
13.
14.
15.
16.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
G
A
D
F
B
H
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
2-1 Using Inductive Reasoning to Make Conjectures
2-1 Using Inductive Reasoning to Make Conjectures
2-2 Conditional Statements
2-2 Conditional Statements
2-1 Using Inductive Reasoning to Make Conjectures
2-2 Conditional Statements
17.
18.
19.
20.
ANS:
ANS:
ANS:
ANS:
F
C
D
B
TOP:
TOP:
TOP:
TOP:
2-2 Conditional Statements
2-2 Conditional Statements
2-2 Conditional Statements
2-2 Conditional Statements
1
ID: A
21. ANS: G
TOP: 2-2 Conditional Statements
22.
23.
24.
25.
26.
27.
28.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
H
A
F
E
B
C
I
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
2-4 Biconditional Statements and Definitions
2-2 Conditional Statements
2-4 Biconditional Statements and Definitions
2-4 Biconditional Statements and Definitions
2-3 Using Deductive Reasoning to Verify Conjectures
2-4 Biconditional Statements and Definitions
2-4 Biconditional Statements and Definitions
29.
30.
31.
32.
33.
ANS:
ANS:
ANS:
ANS:
ANS:
F
D
B
C
G
TOP:
TOP:
TOP:
TOP:
TOP:
2-6 Geometric Proof
2-6 Geometric Proof
2-7 Flowchart and Paragraph Proofs
2-5 Algebraic Proof
2-7 Flowchart and Paragraph Proofs
2