Geometry Chapter 2 Test Review s1
geometry chapter 2 test review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. 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.
____ 2. 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.
____ 3. 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.
____ 4. Which statement is the Law of Detachment?
a. / If is a true statement and q is true, then p is true.b. / If is a true statement and q is true, then is true.
c. / If and are true, then is a true statement.
d. / If is a true statement and p is true, then q is true.
____ 5. Which statement is the Law of Syllogism?
a. / If is a true statement and p is true, then q is true.b. / If is a true statement and q is true, then p is true.
c. / if and are true statements, then is a true statement.
d. / If and are true statements, then is a true statement.
____ 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. 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.
____ 8. How are the two angles related?
a. / vertical / c. / complementaryb. / supplementary / d. / adjacent
Short Answer
9. Identify the hypothesis and conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
10. Write this statement as a conditional in if-then form:
All triangles have three sides.
11. 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 ____.
12. 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.
13. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
14. 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.
15. 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.
16. 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.
17. 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
18. 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.
19. 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.
Fill in each missing reason.
20. 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
21. Given:
Prove:
22. Given:
Prove:
/ a. Given/ b. Addition Property of Equality
/ c. ?
/ d. Substitution Property
23. Given:
Prove x = 21
24. Given:
Prove: x = 3
25. Name the Property of Equality that justifies the statement:
If p = q, then .
26. Name the Property of Congruence that justifies the statement:
If .
27. Name the Property of Congruence that justifies the statement:
If .
Use the given property to complete the statement.
28. Transitive Property of Congruence
If ______.
29. Multiplication Property of Equality
If , then ______.
30. Substitution Property of Equality
If , then ______.
31. bisects = 7x. = . Find
32. Name an angle supplementary to
33. What can you conclude from the information in the diagram?
34. Supplementary angles are two angles whose measures have sum ____.
Complementary angles are two angles whose measures have sum ____.
35. Two angles whose sides are opposite rays are called ____ angles. Two coplanar angles with a common side, a common vertex, and no common interior points are called ____ angles.
36. The complement of an angle is 25°. What is the measure of the angle?
37. and are complementary angles. m = , and m = . Find the measure of each angle.
38. and are supplementary angles. , and . Find the measure of each angle.
39. If and are supplementary angles and , find and
40. Find the value of x.
41. Find
42. Find the values of x and y.
43. What is the negation of this statement?
Miguel’s team won the game.
44. What is the inverse of this statement?
If he speaks Arabic, he can act as the interpreter.
45. 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.
46. 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.
47. 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.
48. 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?
49. Solve for x. Justify each step.
50. Write the inverse of this statement:
If a number is divisible by two, then it is even.
51. Assume that the following statements are true.
i. If Cecil makes his bed, then it is morning.
ii. If it is 8 p.m., then Tami brushes her teeth.
iii. If it is morning, then Ted listens to the radio.
iv. If it is afternoon, then Jeanette takes her daily swim.
v. Cecil makes his bed.
For each statement below, write must be true, may be true, or not true. Use only the information given above. Explain your answers.
a. Ted listens to the radio.
b. Tami does not brush her teeth.
c. Jeanette takes her daily swim.
52. a. Write the following conditional in if-then form.
b. Write its converse in if-then form.
c. Determine the truth value of the original conditional and its converse. Explain why each of them is true or false, and provide a counterexample(s) for any false statement(s).
On a number line, the points with coordinates –2 and 5 are 7 units apart.
53. Give a convincing argument that the following statement is true.
If two angles are congruent and complementary, then the measure of each is 45.
geometry chapter 2 test review
Answer Section
MULTIPLE CHOICE
1. D
2. D
3. C
4. D
5. C
6. B
7. D
8. B
SHORT ANSWER
9. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular.
10. If a figure is a triangle, then it has three sides.
11. conditional; hypothesis; conclusion
12. The number is divisible by 3.
13. If the coordinates of a point are positive, then the point is in the first quadrant.
14. If an angle has measure 90, then it is a right angle.
True
15. =
16. not possible
17. 3x – 4 = 5
18. If a number is a multiple of 64, then it is a multiple of 2.
19. Smiley is too heavy for the bridge.
20. Angle Addition Postulate; Addition Property of Equality
21. a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Division Property of Equality
e. Symmetric Property of Equality
22. Angle Addition Postulate
23. a. Angle Addition Postulate
b. Substitution Property
c. Distributive Property
d. Simplify
e. Addition Property of Equality
f. Division Property of Equality
24. a. Segment Addition Postulate
b. Substitution
c. Simplify
d. Subtraction Property of Equality
e. Division Property of Equality
25. Subtraction Property
26. Symmetric Property
27. Transitive Property
28.
29.
30.
31. 175
32.
33. 1.
2.
3. are vertical angles
34. 180; 90
35. vertical; adjacent
36. 65°
37. = 52, = 38
38.
39. 144, 36
40. –19
41. 37
42. x = 15, y = 17
43. Miguel’s team did not win the game.
44. If he does not speak Arabic, he can’t act as the interpreter.
45. If x2 = 16, then x = 4. False; if x2 = 16, then x can be equal to –4.
46. Not possible. Explanations may vary. Sample: To use the Law of Detachment, you must know that the hypothesis is true.
47. If an angle is straight, then its measure is 180.
Conclusion: is 180.
48. It is safe to remove the sink faucet.
49.
/ Given/ Addition Property of Equality
/ Simplify
/ Division Property of Equality
x = 27 / Simplify
50. If a number is not divisible by two¸ then it is not even.
51.
[4] / a. Must be true. Explanations may vary. Sample: By the Law of Syllogism, “Cecil makes his bed” implies “It is morning,” which implies “Ted listens to the radio.”OR an equivalent explanation using the Law of Detachment
b. May be true. Explanations may vary. Sample: “Cecil makes his bed” implies “It is morning.” You know that Tami brushes her teeth at 8 p.m., but you do not know whether or not she brushes her teeth in the morning.
c. Not true. Explanations may vary. Sample: “Jeanette takes her daily swim” implies that Jeanette swims once per day, so you know that she does not swim in the morning.
[3] / two parts correct with correct explanation
[2] / one part correct with correct explanation OR two parts correct with incomplete explanations
[1] / correct answers with no explanations
52. a. On a number line, if points have coordinates –2 and 5, then they are 7 units apart.
b. On a number line, if points are 7 units apart, then they have coordinates –2 and 5.
c. The original conditional is true by the Ruler Postulate. The converse is false. The points 0 and 7 and 7 units apart, but their coordinates are not –2 and 5.
53. Explanations may vary. Sample: If two angles are congruent and complementary, they have equal measures that add to 90. Thus, each angle has a measure that is one-half of 90, or 45.