____1.What Is the Conclusion of the Following Conditional?

GEOM CH. 2 REVIEW

____1.What is the conclusion of the following conditional?

A number is divisible by 2 if the number is even.

A. / The sum of the digits of the number is divisible by 2.
B. / If a number is even, then the number is divisible by 2.
C. / The number is even.
D. / The number is divisible by 2.

____2.Identify the hypothesis and conclusion of this conditional statement:

If two lines intersect at right angles, then the two lines are perpendicular.

A. / Hypothesis: The two lines are perpendicular.
Conclusion: Two lines intersect at right angles.
B. / Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are perpendicular.
C. / Hypothesis: The two lines are not perpendicular.
Conclusion: Two lines intersect at right angles.
D. / Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are not perpendicular.

____3.Which choice shows a true conditional, with the hypothesis and conclusion identified correctly?

A. / Yesterday was Monday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Monday.
B. / If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is not Thursday.
C. / If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is Thursday.
D. / Yesterday was Tuesday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Tuesday.

____4.Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the ____ , and the part following then is the ____.

A. / conditional; conclusion; hypothesis / C. / conditional; hypothesis; conclusion
B. / hypothesis; conclusion; conditional / D. / hypothesis; conditional; conclusion

____5.Write this statement as a conditional in if-then form:

All triangles have three sides.

A. / If a triangle has three sides, then all triangles have three sides.
B. / If a figure has three sides, then it is not a triangle.
C. / If a figure is a triangle, then all triangles have three sides.
D. / If a figure is a triangle, then it has three sides.

____6.Draw a Venn diagram to illustrate this conditional:

Cars are motor vehicles.

A. / / C. /
B. / / D. /

____7.A conditional can have a ____ of true or false.

A. / hypothesis / C. / counterexample
B. / truth value / D. / conclusion

____

8. Which statement is a counterexample for the following conditional?

If you live in Springfield, then you live in Illinois.

A. / Sara Lucas lives in Springfield.
B. / Jonah Lincoln lives in Springfield, Illinois.
C. / Billy Jones lives in Chicago, Illinois.
D. / Erin Naismith lives in Springfield, Massachusetts.

____9.What is the converse of the following conditional?

If a point is in the fourth quadrant, then its coordinates are negative.

A. / If a point is in the fourth quadrant, then its coordinates are negative.
B. / If a point is not in the fourth quadrant, then the coordinates of the point are not negative.
C. / If the coordinates of a point are not negative, then the point is not in the fourth quadrant.
D. / If the coordinates of a point are negative, then the point is in the fourth quadrant.

____10.Which conditional has the same truth value as its converse?

A. / If x = 7, then .
B. / If a figure is a square, then it has four sides.
C. / If x – 17 = 4, then x = 21.
D. / If an angle has a measure of 80, then it is acute.

____11.For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.

If x = 7, then x2 = 49.

A. / If x2 = 49, then x = 7. True; x2 = 49 if and only if x = 7.
B. / If x2 = 49, then x = 7. True; x = 7 if and only if x2 = 49.
C. / If x2 = 49, then x = 7. False
D. / If x2 = 7, then x = 49. False

____12.What is the converse of the following true conditional? If the converse is true, rewrite the statements as a biconditional. If either is false, give a counterexample.

If two lines are parallel, they do not intersect.

A. / If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
B. / If two lines do not intersect, they are parallel. One statement is false. If two lines are parallel, they may intersect twice.
C. / If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
D. / If two lines do not intersect, they are not parallel. Both statements are true. Two lines are not parallel if (and only if) they do not intersect.

____13.When a conditional and its converse are true, you can combine them as a true ____.

A. / counterexample / C. / unconditional
B. / biconditional / D. / hypothesis

____14.Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.

If an angle is a right angle, its measure is 90.

If an angle measure is 90, the angle is a right angle.

A. / One statement is false. If an angle measure is 90, the angle may be a vertical angle.
B. / One statement is false. If an angle is a right angle, its measure may be 180.
C. / Both statements are true. An angle is a right angle if (and only if) its measure is 90.
D. / Both statements are true. The measure of angle is 90 if (and only if) it is not a right angle.

____15.Write the two conditional statements that make up the following biconditional.

I drink juice if (and only if) it is breakfast time.

A. / I drink juice if (and only if) it is breakfast time.
It is breakfast time if (and only if) I drink juice.
B. / If I drink juice, then it is breakfast time.
If it is breakfast time, then I drink juice.
C. / If I drink juice, then it is breakfast time.
I drink juice only if it is breakfast time.
D. / I drink juice.
It is breakfast time.

____16.Is the following definition of dog reversible? If yes, write it as a true biconditional.

A dog is a mammal.

A. / The reverse is false.
B. / The reverse is true. An animal is a dog if (and only if) it is a mammal.
C. / The reverse is true. An animal is a mammal if (and only if) it is a dog.
D. / The reverse is true. If an animal is a dog, then it is a mammal.

____

17. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.

Two lines that intersect at right angles are perpendicular.

A. / The statement is not reversible.
B. / Yes; if two lines intersect at right angles, then they are perpendicular.
C. / Yes; if two lines are perpendicular, then they intersect at right angles.
D. / Yes; two lines intersect at right angles if (and only if) they are perpendicular.

____18.Is the statement a good definition? If not, find a counterexample.

A square is a figure with two pairs of parallel sides and four right angles.

A. / The statement is a good definition.
B. / No; a rhombus is a counterexample.
C. / No; a rectangle is a counterexample.
D. / No; a parallelogram is a counterexample.

____19.One way to show that a statement is NOT a good definition is to find a____.

A. / converse / C. / biconditional
B. / conditional / D. / counterexample

____20.Which statement provides a counterexample to the following faulty definition?

A square is a figure with four congruent sides.

A. / A six-sided figure can have four sides congruent.
B. / Some triangles have all sides congruent.
C. / A square has four congruent angles.
D. / A rectangle has four sides.

____21.Which biconditional is NOT a good definition?

A. / A whole number is even if and only if it is divisible by 2.
B. / A whole number is odd if and only if the number is not divisible by 2.
C. / An angle is straight if and only if its measure is 180.
D. / A ray is a bisector of an angle if and only if it splits the angle into two angles.

____22.What is the value of x? Identify the missing justifications.

, , and .

/ a.______
x – 5 + x – 7 = 100 / b. Substitution Property
2x – 12 = 100 / c. Simplify
2x = 112 / d.______
x = 56 / e. Division Property of Equality
A. / Angle Addition Postulate; Subtraction Property of Equality
B. / Angle Addition Postulate; Addition Property of Equality
C. / Protractor Postulate; Addition Property of Equality
D. / Protractor Postulate; Subtraction Property of Equality

____23. bisects = 7x. = . Find

A. / 108 / B. / 72 / C. / 180 / D. / 252

____24.Name the Property of Equality that justifies this statement:

If l = m, then .

A. / Multiplication Property / C. / Subtraction Property
B. / Symmetric Property / D. / Transitive Property

____25.Which statement is an example of the Addition Property of Equality?

A. / If p = q then . / C. / If p = q then.
B. / If p = q then . / D. / p = q

Use the given property to complete the statement.

____26.Transitive Property of Congruence

If ______.

A. / / C. /
B. / / D. /

____27.Multiplication Property of Equality

If , then ______.

A. / / C. /
B. / / D. /

____28.Substitution Property of Equality

If , then ______.

A. / / C. /
B. / / D. /

____29.Name the Property of Congruence that justifies the statement:

If .

A. / Symmetric Property / C. / Reflexive Property
B. / Transitive Property / D. / none of these

____30.Name the Property of Congruence that justifies this statement:

If .

A. / Transitive Property / C. / Reflexive Property
B. / Symmetric Property / D. / none of these

____31.Complete the two-column proof.

Given:

Prove:

33. What is the value of x?

A. / –16 / B. / 120 / C. / 60 / D. / 16

____34.What is the value of x?

A. / 84 / B. / 36 / C. / 120 / D. / 60

____35. Find

A. / 150 / B. / 30 / C. / 160 / D. / 20

____

36. Find the values of x and y.

A. / x = 15, y = 17 / C. / x = 68, y = 112
B. / x = 112, y = 68 / D. / x = 17, y = 15

37.Write the conditional statement that the Venn diagram illustrates.

38.Is the following conditional true or false? If it is true, explain why. If it is false, give a counterexample.

If it is snowing in Dallas, Texas, then it is snowing in the United States.

39.Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.

If x = 4, then x2 = 16.

____40.What is the converse and the truth value of the converse of the following conditional?

If an angle is a right angle, then its measure is 90.

A. / If an angle is not a right angle, then its measure is 90.
False
B. / If an angle is not a right angle, then its measure is not 90.
True
C. / If an angle has a measure of 90, then it is a right angle.
False
D. / If an angle has a measure of 90, then it is a right angle.
True

41.Write the converse of the given true conditional and decide whether the converse is true or false. If the converse is true, combine it with the conditional to form a true biconditional. If the converse is false, give a counterexample.

If the probability that an event will occur is 0, then the event is impossible to occur.

42.For the given statements below, write the first statement as a conditional in if-then form. Then, if possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Explain.

A straight angle has a measure of 180.

is a straight angle.

43.A plumber knows that if you shut off the water at the main valve, it is safe to remove the sink faucet. The plumber turns the main valve to the “off” position. What conclusion can the plumber make?

44.Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state not possible. Explain.

Statement 1: If two lines intersect, then they are not parallel.

Statement 2: do not intersect.

45. What is the value of x? Identify the missing justifications.

46.Solve for x. Justify each step.

47.What is the value of x? Justify each step.

48.Complete the paragraph proof.

Given: are supplementary, and are supplementary.

Prove:

By the definition of supplementary angles, _____(a) and _____(b). Then by _____(c). Subtract from each side. You get _____(d), or _____(e).

Answer Section

1.ANS:D

2.ANS:B

3.ANS:D

4.ANS:C

5.ANS:D

6.ANS:A

7.ANS:B

8.ANS:D

9.ANS:D

10.ANS:C

11.ANS:C

12.ANS:A

13.ANS:B

14.ANS:C

15.ANS:B

16.ANS:A

17.ANS:D

18.ANS:C

19.ANS:D

20.ANS:A

21.ANS:D

22.ANS:B

23.ANS:D

24.ANS:B

25.ANS:B

26.ANS:D

27.ANS:A

28.ANS:B

29.ANS:A

31.ANS:A

32.ANS:B

33.ANS:D

34.ANS:D

35.ANS:B

36.ANS:A

37.ANS:

If a figure is a square, then it is a quadrilateral.

38.ANS:

True. Dallas, Texas is a city that lies within the United States.

39.ANS:

If x2 = 16, then x = 4. False; if x2 = 16, then x can be equal to –4.

40.ANS:D

41.ANS:

If an event is impossible, the probability of the event is 0.

True

An event is impossible if and only if the probability of the event is zero.

42.ANS:

If an angle is straight, then its measure is 180.

Conclusion: is 180.

43.ANS:

It is safe to remove the sink faucet.

44.ANS:

Not possible. Explanations may vary. Sample: To use the Law of Detachment, you must know that the hypothesis is true.

45.ANS:

a. Angle Addition Postulate

b. Substitution Property

c. Distributive Property

d. Simplify

e. Addition Property of Equality

f. Division Property of Equality

46.ANS:

/ Given
/ Addition Property of Equality
/ Simplify
/ Division Property of Equality
x = 27 / Simplify

47.ANS:

a. Segment Addition Postulate

b. Substitution

c. Simplify

d. Subtraction Property of Equality

e. Division Property of Equality

48.ANS:

a. 180

b. 180

c. Transitive Property (or Substitution Property)

d.

e.