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Post-Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Make a conjecture about the next object in this sequence.

a.		c.
b.		d.

Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: points A, B, C, and D
Conjecture: A, B, C, and D are coplanar.

a.	False; three points are always coplanar but four are not.
b.	False; two points are always coplanar but four are not.
c.	True
d.	False; the four points do not have to be in a straight line.

Given:

Conjecture:

a.	False;	c.	False;
b.	True	d.	False;

Given: Two angles are supplementary.
Conjecture: They are both acute angles.

a.	True
b.	False; either both are right or they are adjacent.
c.	False; they must be vertical angles.
d.	False; either both are right or one is obtuse.

Identify the conclusion of the statement Jack will go to school if today is Monday.

a.	Jack will go to school	c.	today is not Monday
b.	today is Monday	d.	Jack will not go to school

Write a conditional statement from the statement.
A horse has 4 legs.

a.	If it has 4 legs then it is a horse.	c.	It has 4 legs and it is a horse.
b.	Every horse has 4 legs.	d.	If it is a horse then it has 4 legs.

Fill in each missing reason.

Given:
Prove:

a.	a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality	c.	a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Symmetric Property of Equality
b.	a. Given b. Substitution Property c. Subtraction Property of Equality d. Addition Property of Equality e. Symmetric Property of Equality	d.	a. Given b. Symmetric Property of Equality c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality

Which best describes the statement If two planes intersect, then their intersection is a point?

a.	sometimes true	c.	always true
b.	cannot tell	d.	never true

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 logical reasoning from scientific research, 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 deductive reasoning.
d.	Since the conclusion is based on a pattern of observation, it is a result of inductive reasoning.

Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

10.

A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.

a.	A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. True
b.	A non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. False; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional.
c.	A non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. True
d.	A statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. False; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional.

Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.

11.

(1) You are in ninth grade.
(2) People who are in ninth grade floss their teeth regularly.
(3) You floss your teeth regularly.

a.	yes; Law of Detachment
b.	yes; Law of Syllogism
c.	invalid

Use the figure below.

12.

If mÐAFB

10 and mÐBFC

20, find x.

a.	10	c.	23.3
b.	21.25	d.	15

13.

Identify the hypothesis and conclusion of the conditional statement.
If it is raining then it is cloudy.

a.	Hypothesis: Clouds make rain. Conclusion: Rain does not make clouds.
b.	Hypothesis: Rain and clouds happen together. Conclusion: Rain and clouds do not happen together..
c.	Hypothesis: It is raining. Conclusion: It is cloudy.
d.	Hypothesis: It is cloudy. Conclusion: It is raining.

14.

Choose the property that justifies the following statement.
If x

2 and x

3, then 2

a.	Substitution	c.	Symmetric
b.	Reflexive	d.	Transitive

Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample.

15.

All Jack Russells are terriers.

a.	If a dog is a terrier, then a dog is a terrier. True
b.	If it is a Jack Russell, then a dog is a terrier. True
c.	If a dog is a terrier, then it is a Jack Russell. False; it could be a Scottish terrier.
d.	All Jack Russells are terriers. True

16.

Show that the conjecture is false by finding a counterexample.
If

, then

a.	,	c.	,
b.	,	d.	,

Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

17.

All quadrilaterals are four-sided figures.

a.	All four-sided figures are quadrilaterals. True
b.	All non-quadrilaterals are four-sided figures. False; a triangle is a non-quadrilateral.
c.	No four-sided figures are not quadrilaterals. True
d.	No quadrilaterals are not four-sided figures. True

18.

Which law can be used to determine that statement (3) is a valid conclusion to statements (1) and (2)?
(1) If an angle is acute, then it cannot be obtuse.
(2) ÐA is acute.
(3) ÐA cannot be obtuse.