Free Printable Unit 2 Review Logic and Reasoning

1.

Which is a counterexample to the following statement?

If $\overline{LM}\cong\overline{MN}$ , then $M$ is the midpoint of $\overline{LN}$ .

a)

b)

c)

d)

None of these

2.

What is the relationship between the statements?

a)

Statement 2 is the inverse of statement 1

b)

Statement 2 is the converse of statement 1

c)

Statement 2 is the biconditional of statement 1

d)

Statement 2 is the contrapositive of statement 1

3.

If $\overline{AB}\cong\overline{BC}\ and\ \overline{BC}\cong\overline{CD}$ , which property shows

a

\overline{AB}\cong\overline{CD}

a)

Substitution Property

b)

Reflexive Property

c)

Symmetric Property

d)

Transitive Property

4.

If $\overline{QR}\cong\overline{ST}$ , $QR=\frac{2}{3}x\ \ inches$ , and $ST\ =\ 0.4\ \ inches$ , find the value of $x$

a)

x = 2.4

b)

x = 0.6

c)

x = 2

d)

x = 0.3

5.

a)

DG = 2 meters

b)

DG = 11 meters

c)

DG = 10 meters

d)

DG = 19 meters

6.

a)

180

b)

123

c)

93

d)

87

7.

Select all true statements

a)

$\overline{AD}\cong\overline{BC}$

b)

$\overline{AE}\cong\overline{FC}$

c)

$\overline{BC}\cong\overline{EF}$

d)

$\overline{EB}\cong\overline{DF}$

e)

$\overline{EB}\cong\overline{EF}$

8.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

a)

If a polygon is not a quadrilateral, then it is not a trapezoid.

b)

If a polygon is not a trapezoid, then it is not a quadrilateral.

c)

If a polygon is a trapezoid, then it is a quadrilateral.

d)

A rectangle is also a quadrilateral.

9.

The statement "an angle is a right angle if and only if its measure is 90^o" is an example of what type of statement?

a)

Conditional

b)

Conjecture

c)

Biconditional

10.

Reasoning based on specific examples and patterns used to form conjectures is called ______________ reasoning.

a)

Inductive

b)

Deductive

11.

If it is a number, then it is either positive or negative. What is an appropriate counterexample?

a)

10

b)

-2

c)

0

d)

True. There is no counterexample.

12.

Using the Law of Detachment, draw a conclusion based on the statements given:

If a plane flies to China, then it will be a long flight. Sarah bought a ticket to China.

a)

Sarah will get stuck in the security line.

b)

Sarah will have a long flight.

c)

Sarah will need to bring a neck pillow and headphones.

d)

Sarah will get stuck with a middle seat on the plane.

13.

Using the Law of Syllogism, write a new conditional statement that follows from the pair of true statements.

If you study, then you will pass the test. If you pass the test, then you will pass the class.

a)

If you study, then you will pass the class.

b)

If you pass the test, then you should study.

c)

If you pass the class, then you will pass the test.

d)

If you study, then you will pass the test.

14.

Fill in the blank with the missing statement in the proof: (a)

Choose from the below words

$m∠ABD=m∠DBC$

$m∠ABC=m∠ABC$

none of the other choices are correct

$m\angle ABD+m\angle DBC=m\angle ABC$

15.

What allows to say that angle IKH is congruent to angle GKJ?

a)

Definition of vertical angles

b)

Linear Pairs Theorem

c)

Definition of a straight angle

d)

Vertical angles theorem

16.

In this proof, reason 2 should be

(a) and reason 3 should be (b)

Choose from the below words

Definition of Congruent Angles

Vertical Angles

Transitive Property

Given

Vertical Angles Theorem

17.

In this proof, reason 2 should be (a) , reason 3 should be (b) and reason 4 should be (c)

Choose from the below words

Subtraction POE

Addition POE

Division POE

Distributive POE

Transitive POE

18.

A _________ is a statement that is accepted as true without proof.

a)

theorem

b)

postulate

c)

argument

d)

proof

19.

A _________ is a statement that is proven to be true for all cases.

a)

theorem

b)

postulate

c)

argument

d)

proof

20.

Which of the following can be used as reasons in a proof? Select all that apply.

a)

Definitions

b)

Algebraic properties

c)

Postulates

d)

Theorems

e)

Conjectures

21.

Identify the correct reason for the statement.

a)

Substitution postulate

b)

Definition of angle bisector

c)

Angle addition postulate

d)

Angle bisector theorem

22.

In order to solve for x in this diagram, what theorem would you need to use?

a)

The transitive property

b)

Linear pair theorem

c)

Vertical Angles Congruence Theorem

d)

Right angles congruence theorem

23.

Two intersecting lines are shown in the diagram. Solve for x.

a)

𝑥=10

b)

𝑥=−10

c)

𝑥≈7.89

d)

𝑥≈1.83

Unit 2 Review Logic and Reasoning

Total questions: 23

Worksheet time: 31mins

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