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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 are noncollinear. |
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B. |
A, B, and C are collinear. |
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C. |
A, B, and C form a right triangle. |
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D. |
A, B, and C form on equilateral triangle. |
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Hint |
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2. |
In the figure, ABCD is a square. Which of the following is a valid conjecture about points A, B, C, and D? |
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A. |
AB = BD |
B. |
AB + CD = 12 |
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C. |
AB = CD |
D. |
None of the statements are valid conjectures. |
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Hint |
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3. |
Determine the converse of the following if-then statement. If the flowers are yellow, then they are daffodils. |
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A. |
If the flowers are not yellow, then they are not daffodils. |
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B. |
The flowers are not daffodils. |
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C. |
The flowers are not yellow. |
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D. |
If the flowers are daffodils, then they are yellow. |
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Hint |
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4. |
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 noncollinear. |
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B. |
If three points form a triangle, then they are noncollinear. |
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C. |
If three points do not form a triangle, then they are not noncollinear. |
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D. |
If three points are not noncollinear, then they do not form a triangle. |
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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 Detachment |
B. |
Law of Deductive Reasoning |
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C. |
Law of Syllogism |
D. |
Law of Conditional |
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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 even, 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 odd, 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. |
Which statement shows the Transitive Property of Equality? |
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A. |
If AB = CD and AB =EF, then  |
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B. |
If and then  |
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C. |
If AB + BC = DE + BC, then AB = DE. |
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D. |
If AB = CD, then CD = AB. |
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Hint |
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8. |
Complete the proof. |
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A. |
Addition Property (=) |
B. |
Substitution Property (=) |
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C. |
Transitive Property |
D. |
Angle Addition Property |
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Hint |
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9. |
If and form a linear pair and find  |
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A. |
106 |
B. |
76 |
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C. |
86 |
D. |
96 |
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Hint |
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10. |
If and are vertical angles and and find  |
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A. |
23 |
B. |
43 |
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C. |
68 |
D. |
72 |
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Hint |
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11. |
What three things are accepted as true without verification or proof? |
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A. |
theorems, postulates, and undefined terms |
B. |
definitions, theorems, and postulates |
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C. |
conclusions, hypotheses, and postulates |
D. |
definitions, postulates, and undefined terms. |
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Hint |
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12. |
For the proof shown, provide statement 3. |
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A. |
AB = CD |
B. |
AB = EF |
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C. |
CD = EF |
D. |
AB = BA |
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Hint |
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13. |
For the proof shown, provide the reason for part d. |
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A. |
Symmetric Property (=) |
B. |
Definition of congruent segments |
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C. |
Definition of Addition |
D. |
Definition of a line |
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Hint |
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14. |
A __________ is a compound statement formed by joining two or more statements with the word and. |
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A. |
truth value |
B. |
disjunction |
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C. |
conjunction |
D. |
negation |
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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. |
14 |
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C. |
25 |
D. |
1 |
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Hint |
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16. |
A _________ is a statement that describes a fundamental relationship between the basic terms of geometry and is accepted as true. |
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A. |
proof |
B. |
theorem |
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C. |
postulate |
D. |
definition |
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Hint |
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