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1. |
A ______________ is a logical argument in which each statement is backed up by a statement that is accepted as true. |
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A. |
postulate |
B. |
theorem |
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C. |
proof |
D. |
definition |
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Hint |
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2. |
Determine if the following conjecture is true or false? Explain. Given: x2 = 4
Conjecture: x = 4 or x = -4 |
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A. |
False; the square root of 4 is 2 or -2. |
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B. |
True; squaring a positive number results in a positive number and squaring a negative number results in a positive number. |
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C. |
True; two answers are always more accurate than one answer. |
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D. |
False; the square root of a positive number is always a positive number. |
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Hint |
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3. |
''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. |
The sum of 8 and 24 must be even. |
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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. |
If the numbers 8 and 24 are odd, then their sum is 32. |
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Hint |
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4. |
Name the postulate or theorem that concludes  |
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A. |
Consecutive Interior Angles Theorem |
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B. |
Corresponding Angles Postulate |
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C. |
Alternate Exterior Angles Theorem |
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D. |
Alternate Interior Angles Theorem |
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Hint |
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5. |
If     , and  what is the measure of  |
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A. |
72 |
B. |
108 |
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C. |
180 |
D. |
76 |
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Hint |
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6. |
Find the distance between the parallel lines m and n whose equations are
y = x + 4 and y = x - 6, respectively. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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7. |
Which pair of triangles is congruent by the SSS Postulate? |
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A. |
 with vertices A(-2, -4), B(-6, 3), and
C(-2, 3) and  with vertices D(3, 1), E(3, 6),
and F(-2, 6) |
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B. |
with vertices A(3, 3), B(3, 7), and C(-1, 7)
and with vertices D(0, 5), E(4, 5), and F(4, -2) |
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C. |
with vertices A(0, 2), B(-4, 2), and C(-4, -3)
and with vertices D(1, 1), E(1, 5), and F(6, 5) |
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D. |
with vertices A(0, 7), B(0, 0), and C(-3, 0)
and with vertices D(5, 5), E(-2, 5), and F(-2, -2) |
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Hint |
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8. |
Name the property that justifies if AB < BC and BC < CD,
then AB < CD. |
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A. |
Addition Property |
B. |
Comparison Property |
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C. |
Division Property |
D. |
Transitive Property |
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Hint |
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9. |
Which of the following statements is true? |
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A. |
The intersection of  and plane M is  . |
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B. |
intersects plane M at point C. |
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C. |
intersects plane M at point B. |
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D. |
intersects plane M in two points. |
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Hint |
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10. |
Find XY on the number line shown. |
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A. |
-7 |
B. |
7 |
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C. |
0 |
D. |
4 |
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Hint |
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11. |
Which law is similar to the Transitive Property? |
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A. |
Law of Syllogism |
B. |
Law of Detachment |
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C. |
Law of Deductive Reasoning |
D. |
Law of Conditional |
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Hint |
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12. |
''If two angles are vertical, then they are congruent.'' is a true conditional, and  1 and 2 are vertical. Which is not true based on the Law of Detachment? |
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A. |
1 and 2 are not congruent. |
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B. |
1 and 2 both have a measure of 45. |
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C. |
Both1 and 2 are obtuse. |
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D. |
1 and 2 are congruent. |
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Hint |
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13. |
For the proof shown, provide statement 3. |
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A. |
AB = BA |
B. |
AB = EF |
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C. |
AB = CD |
D. |
CD = EF |
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Hint |
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14. |
Name a pair of consecutive interior angles. |
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A. |
4 and 6 |
B. |
10 and 8 |
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C. |
6 and 7 |
D. |
10 and 9 |
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Hint |
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15. |
Assuming two parallel lines are cut by a transversal, which types of angles are not necessarily congruent? |
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A. |
vertical angles |
B. |
alternate interior angles |
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C. |
consecutive interior angles |
D. |
corresponding angles |
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Hint |
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16. |
If line m and n are parallel and l is perpendicular to m, then ______. |
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A. |
l is perpendicular to n. |
B. |
l is parallel to n. |
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C. |
l and n are skew lines. |
D. |
m is parallel to n. |
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Hint |
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17. |
Find the value of x. |
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A. |
14 |
B. |
10 |
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C. |
40 |
D. |
42 |
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Hint |
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18. |
How many other triangles in the figure appear to be congruent to  ABC? |
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A. |
8 |
B. |
3 |
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C. |
4 |
D. |
7 |
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Hint |
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19. |
Graph the line with a slope of  and a y-intercept of –3. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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20. |
Find the length of the hypotenuse of this right triangle. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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