| |
| |
1. |
Name two lines that lie in plane ADH. |
| |
|
 |
| |
|
A. |
 ,  |
B. |
 ,  |
| |
|
C. |
 ,  |
D. |
 , |
| |
|
Hint |
|
| |
2. |
Which figure shows points D(-1, -1), E(3, 4), F(-4, 2), and G(0, 2) on a coordinate plane with lines EF and DG intersecting at H and a point C that is coplanar with D, E, F, G, and H, but is not contained in either line? |
| |
|
A. |
 |
| |
|
B. |
 |
| |
|
C. |
 |
| |
|
D. |
 |
| |
|
Hint |
|
| |
3. |
Which of the following best describes  |
| |
|
 |
| |
|
A. |
acute |
B. |
straight |
| |
|
C. |
obtuse |
D. |
right |
| |
|
Hint |
|
| |
4. |
Which law states that if a conditional is true and its hypothesis is true, then the conclusion is true? |
| |
|
A. |
Law of Conditional |
B. |
Law of Detachment |
| |
|
C. |
Law of Deductive Reasoning |
D. |
Law of Syllogism |
| |
|
Hint |
|
| |
5. |
The Law of Detachment and other laws of logic can be used to provide a system for reaching logical conclusions, called _____________. |
| |
|
A. |
detachment reasoning |
B. |
reasonable doubt |
| |
|
C. |
inductive reasoning |
D. |
deductive reasoning |
| |
|
Hint |
|
| |
6. |
Which statement follows from statements (1) and (2) by the Law of Syllogism? (1) If an object is a square, then it is a rhombus.
(2) If an object is a rhombus, then it is an equilateral. |
| |
|
A. |
An object is a square. |
B. |
If an object is an equilateral, then it is a square. |
| |
|
C. |
If an object is a square, then it is an equilateral. |
D. |
An object is a rhombus. |
| |
|
Hint |
|
| |
7. |
''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. |
| |
|
A. |
If the numbers 8 and 24 are odd, then their sum is 32. |
| |
|
B. |
The sum of 8 and 24 must be even. |
| |
|
C. |
If the numbers 8 and 24 are even, then their sum is 32. |
| |
|
D. |
The sum of 8 and 24 must be odd. |
| |
|
Hint |
|
| |
8. |
Find the number of different segments formed by 8 collinear points. |
| |
|
A. |
27 |
B. |
21 |
| |
|
C. |
28 |
D. |
36 |
| |
|
Hint |
|
| |
9. |
For the proof shown, provide statement 5. |
| |
|
 |
| |
|
 |
| |
|
A. |
BC = EF |
B. |
AC = DF |
| |
|
C. |
AB = DE |
D. |
AB = EF |
| |
|
Hint |
|
| |
10. |
In the figure shown,  is complementary to  and is complementary to  . Which statement is true if none of the measures of the angles equal 45? |
| |
|
 |
| |
|
A. |
 |
B. |
is complementary to itself. |
| |
|
C. |
is complementary to . |
D. |
|
| |
|
Hint |
|
| |
11. |
Find XY on the number line shown. |
| |
|
 |
| |
|
A. |
7 |
B. |
0 |
| |
|
C. |
4 |
D. |
-7 |
| |
|
Hint |
|
| |
12. |
Find the coordinates of R, the midpoint of  , if the endpoints of are Q(3, -5) and S(-3, 6). |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
(6,1) |
| |
|
Hint |
|
| |
13. |
Which statement follows from (1) and (2) by the Law of Syllogism? (1) If two angles form a linear pair, then they are supplementary. (2) If two angles are supplementary, then the sum of their measures is 180. |
| |
|
A. |
Supplementary angles form a linear pair. |
| |
|
B. |
The measures of supplementary angles add up to 180. |
| |
|
C. |
The sum of the measures of the angles in a linear pair is 180. |
| |
|
D. |
A linear pair is formed by supplementary angles. |
| |
|
Hint |
|
| |
14. |
Using the following true conditional and hypothesis, which statement would follow from the Law of Detachment?A square has four right angles. WXYZ is a square. |
| |
|
A. |
If WXYZ is not a square, then it has four right angles. |
| |
|
B. |
If WXYZ is not a square, then it does not have four right angles. |
| |
|
C. |
If WXYZ has four right angles, then it is a square. |
| |
|
D. |
WXYZ has four right angles. |
| |
|
Hint |
|
| |
15. |
For the proof shown, provide the reason for part b. |
| |
|
 |
| |
|
 |
| |
|
A. |
Definition of congruent segments |
B. |
Symmetric Property (=) |
| |
|
C. |
Definition of a line |
D. |
Definition of Addition |
| |
|
Hint |
|
| |
16. |
What three properties hold true for congruence of segments? |
| |
|
A. |
addition, subtraction, and multiplication |
| |
|
B. |
reflexive, symmetric, and substitution |
| |
|
C. |
reflexive, multiplication, and division |
| |
|
D. |
reflexive, symmetric, and transitive |
| |
|
Hint |
|
| |
17. |
What is an acceptable range for a measurement of 60.5 centimeters? |
| |
|
A. |
60.25 cm to 60.75 cm |
B. |
604.5 mm to 605.5 mm |
| |
|
C. |
604 mm to 606 mm |
D. |
60 cm to 61 cm |
| |
|
Hint |
|
| |
18. |
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 both Spanish and French? |
| |
|
 |
| |
|
A. |
40 |
B. |
15 |
| |
|
C. |
55 |
D. |
1 |
| |
|
Hint |
|
| |
19. |
Which of the following statements is not a postulate? |
| |
|
A. |
Through any two points, there is exactly one line. |
| |
|
B. |
If two lines intersect, then their intersection is exactly one point. |
| |
|
C. |
A plane contains at least three points not on the same line. |
| |
|
D. |
Points that lie of the same plane are said to be coplanar. |
| |
|
Hint |
|
| |
20. |
If and form a linear pair and m = 72, find m. |
| |
|
 |
| |
|
A. |
18 |
B. |
144 |
| |
|
C. |
72 |
D. |
108 |
| |
|
Hint |
|
|
|