Geometry Chapter 2 Review
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____1.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.
____2.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.
____3.Which biconditional is NOT a good definition?
a. / A whole number is odd if and only if the number is not divisible by 2.b. / An angle is straight if and only if its measure is 180.
c. / A whole number is even if and only if it is divisible by 2.
d. / A ray is a bisector of an angle if and only if it splits the angle into two angles.
____4.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.
____5.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 measure 80, then it is acute.
____6.Which statement is an example of the Addition Property of Equality?
a. / If p = q then / c. / If p = q thenb. / If p = q then . / d. / p = q
____7.How are the two angles related?
a. / vertical / c. / complementaryb. / supplementary / d. / adjacent
____8.In the figure shown, . Which of the following statements is false?
Not drawn to scale
a. /b. / BEC and CED are adjacent angles.
c. /
d. / AED and BEC are adjacent angles.
____9.Complete the paragraph proof.
Given: and are right angles.
Prove:
By the definition of ____, . By the _____ Property, , or .
a. / complementary angles; Substitutionb. / right angles; Substitution
c. / complementary angles; Reflexive
d. / right angles; Symmetric
Short Answer
10.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.
11.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.
12.Solve for x. Justify each step.
13.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.
14.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.
15.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?
Fill in each missing reason.
16. Given:
17.Given:
18.Given:
Prove:
19 . Given:, , and .
Find x.
/ a. _____x – 5 + x – 11 = 100 / b. Substitution Property
2x – 16 = 100 / c. Simplify
2x = 116 / d. _____
x = 58 / e. Division Property of Equality
20. Complete the paragraph proof.
Given: are supplementary, and are supplementary.
Prove:
By the definition of supplementary angles, ______and ______. Then by ______. Subtract from each side. You get ______or ______.
21.If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
Statement 1: If x = 3, then 3x – 4 = 5.
Statement 2: x = 3
22. bisects = 7x. = . Find
23. and are complementary angles. m = , and m = . Find the measure of each
angle.
- and are supplementary angles. , and . Find the measure of each angle.
25. If and are supplementary angles and , find and
26. Underline the hypothesis and circle the conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
27. What is the conclusion of the following conditional?
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
28. Draw a Draw a Venn diagram to illustrate this conditional:
Christmas is a holiday.
29. 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.
30. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
31. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 3, then x2 = 9.
32. 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 two lines are parallel, they do not intersect.
If two lines do not intersect, they are parallel.
33. 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.
34. Write the two conditional statements that make up the following biconditional.
I drink juice if and only if it is breakfast time.
35. Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a true biconditional.
Two lines that intersect at right angles are perpendicular.
36. 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.
37. Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are congruent, then they have equal measures.
and are congruent.
38. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
I can go to the concert if I can afford to buy a ticket.
I can go to the concert.
39. Use the Law of Syllogism to draw a conclusion from the two given statements.
If a number is a multiple of 64,then it is a multiple of 8.
If a number is a multiple of 8, then it is a multiple of 2.
40. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.
If an elephant weighs more than 2,000 pounds, then it weighs more than Jill’s car.
If something weighs more than Jill’s car, then it is too heavy for the bridge.
Smiley the Elephant weighs 2,150 pounds.
41. Name the Property of Equality that justifies the statement:
If p = q, then .
42. Name the Property of Congruence that justifies the statement:
If .
43. Name the Property of Congruence that justifies the statement:
If .
Use the given property to complete the statement.
44.Transitive Property of Congruence
If ______.
45.Multiplication Property of Equality
If , then ______.
46.Substitution Property of Equality
If , then ______.
47.Supplementary angles are two angles whose measures have sum ______.
Complementary angles are two angles whose measures have sum ______.
48.Name an angle supplementary to
49.The complement of an angle is 25°. What is the measure of the angle?
50. Find 51. Find the values of x and y. .