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1. |
Make a conjecture based on the following information. For points A, B, and C, AB = 2, BC = 3, and AC = 4. |
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A. |
A, B, and C form a right triangle. |
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B. |
A, B, and C are noncollinear. |
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C. |
A, B, and C form on equilateral triangle. |
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D. |
A, B, and C are collinear. |
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Hint |
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2. |
Marita always listens to her favorite radio station, an oldies station, when she drives her car. Every morning she listens to her radio on the way to school. On Monday, she turns on her car radio and it is playing country music. Which of the following is a valid conjecture for why her radio is playing different music? |
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A. |
A country music station bought out her favorite music station over the weekend. |
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B. |
Her favorite station has changed their morning program to include country music. |
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C. |
All statements are valid conjectures. |
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D. |
Someone used her car during the weekend and changed the station. |
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Hint |
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3. |
Determine the contrapositive of the following if-then statement.
If three points are noncollinear, then they form a triangle. |
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A. |
If three points do not form a triangle, then they are not noncollinear. |
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B. |
If three points form a triangle, then they are noncollinear. |
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C. |
If three points are not noncollinear, then they do not form a triangle. |
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D. |
If three points do not form a triangle, then they are noncollinear. |
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Hint |
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4. |
A ______________ is a diagram that can be used to illustrate a conditional. |
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A. |
bar graph |
B. |
flow chart |
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C. |
tree diagram |
D. |
Venn diagram |
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Hint |
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5. |
Which law states that if a conditional is true and its hypothesis is true, then the conclusion is true? |
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A. |
Law of Conditional |
B. |
Law of Deductive Reasoning |
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C. |
Law of Detachment |
D. |
Law of Syllogism |
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Hint |
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6. |
''If two numbers are even, then their sum is even'' is a true conditional, and 8 and 24 are even numbers. Use the Law of Detachment to reach a logical conclusion. |
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A. |
If the numbers 8 and 24 are odd, then their sum is 32. |
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B. |
The sum of 8 and 24 must be odd. |
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C. |
If the numbers 8 and 24 are even, then their sum is 32. |
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D. |
The sum of 8 and 24 must be even. |
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Hint |
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7. |
Justify step 2 in solving  |
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A. |
Distributive Property (=) |
B. |
Division Property (=) |
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C. |
Multiplication Property (=) |
D. |
Subtraction Property (=) |
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Hint |
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8. |
For the proof shown, provide statement 2. |
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A. |
AC = DE, AB = DF |
B. |
AB = BC, DE = EF |
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C. |
AC = DF, BC = EF |
D. |
AB = DE |
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Hint |
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9. |
For the proof shown, provide the reason for part c. |
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A. |
Addition Property of Equality |
B. |
Subtraction Property of Equality |
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C. |
Division Property of Equality |
D. |
Multiplication Property of Equality |
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Hint |
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10. |
All right angles are ____________. |
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A. |
complementary |
B. |
180° |
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C. |
congruent |
D. |
transitive |
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Hint |
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11. |
Which statement explains why  |
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A. |
Angles complementary to the same angle or to congruent angles are congruent. |
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B. |
Vertical angles are congruent. |
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C. |
Angles adjacent to the same angle or to congruent angles are congruent. |
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D. |
All right angles are congruent. |
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Hint |
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12. |
What is a valid conclusion to the following hypothesis?
If there are two points... |
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A. |
There are an infinite number of lines containing both points. |
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B. |
There is one line containing both points. |
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C. |
There are no lines containing both points. |
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D. |
There are two lines containing both points. |
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Hint |
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13. |
Name the property that justifies the statement. ''If 2x = 12, then x = 6''. |
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A. |
Symmetric Property |
B. |
Multiplication Property (=) |
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C. |
Transitive Property (=) |
D. |
Division Property (=) |
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Hint |
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14. |
Which of the following is not one of the five essential parts needed to construct a good proof? |
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A. |
List the given information. |
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B. |
Assume what you are trying to prove is true. |
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C. |
If possible, draw a diagram to illustrate the given information. |
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D. |
State the theorem to be proved. |
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Hint |
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15. |
The freshman class of 63 students conducted a survey to compare how many students took Spanish as opposed to French as a foreign language. The results are shown in the Venn diagram. How many students studied neither Spanish nor French? |
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A. |
7 |
B. |
25 |
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C. |
14 |
D. |
1 |
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Hint |
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16. |
A group of 7 people get together for a meeting. Before the meeting starts, they each shake hands with every person at the meeting. If a person only shakes hands with another person once, how many handshakes were there before the meeting began? |
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A. |
42 |
B. |
7 |
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C. |
21 |
D. |
15 |
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Hint |
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