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1. |
A _____ is a compound statement formed by joining two statements with the word and. |
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A. |
negation |
B. |
disjunction |
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C. |
conjunction |
D. |
conditional |
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Hint |
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2. |
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A. |
There are 12 months in a year and 12 - 4 = 8. |
B. |
There are 12 months in a year or  . |
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C. |
12 - 4 = 8 and there are not 12 months in a year. |
D. |
There are 12 months in a year and . |
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3. |
Which statement follows from statements (1) and (2) by the Law of Syllogism?
(1) If two adjacent angles form a linear pair, then the sum of the measures of the angles is 180.
(2) If the sum of the measures of two angles is 180, then the angles are supplementary. |
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A. |
If the sum of the measures of two angles is 180, then the angles form a linear pair. |
B. |
If two adjacent angles form a linear pair, then the angles are supplementary. |
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C. |
If two adjacent angles form a linear pair, then the sum of the measures of the angles is 180. |
D. |
If two angles are supplementary, then the sum of the measures of the angles is 180. |
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Hint |
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4. |
The statements ''If Eric reads the book, he will be prepared for the exam'' and ''If Eric is prepared for the exam, he will get a passing grade'' are two conditionals. Use the Law of Syllogism to reach a logical conclusion. |
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A. |
no logical conclusion. |
B. |
If Eric gets a passing grade, then he did prepare for the exam. |
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C. |
If Eric prepares for the exam, then he will read the book. |
D. |
If Eric reads the book, then he will get a passing grade. |
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Hint |
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5. |
If  and  , show that  . |
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A. |
You know that and . Point C is the midpoint of  since . That means that C is also the midpoint of  . So  by definition of midpoint. Therefore, by SSA. |
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B. |
You know that and .  because  and  are congruent alternate interior angles. So, by SAS. |
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C. |
You know that and .  because they are alternate interior angles, and  because they are vertical angles. So, by AAA. |
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D. |
You know that and .  and  are congruent because they are vertical angles. Thus, by ASA. |
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Hint |
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6. |
Write a paragraph proof to prove  . |
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A. |
There is not enough information provided, so it is not possible to prove . |
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B. |
Quadrilateral PQRS is a parallelogram because both pairs of opposite sides are parallel. Opposite sides of a parallelogram are congruent, so  and  . Also, opposite angles of parallelograms are congruent so  . Therefore, by SAS. |
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C. |
Quadrilateral PQRS is a parallelogram because both pairs of opposite sides are parallel.  and  because they are alternate interior angles. Also, because they are opposite angles of a parallelogram. Thus, by AAA. |
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D. |
Quadrilateral PQRS is a parallelogram because both pairs of opposite sides are parallel. Since quadrilateral is a parallelogram, by definition. |
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Hint |
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7. |
What is the first statement written in a two-column proof of the following?
Given: 
Prove:  |
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B. |
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C. |
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D. |
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Hint |
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8. |
What is the reason for the conclusion of the proof below?
Given: 
Prove:  |
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A. |
Definition of midpoint |
B. |
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C. |
CPCTC |
D. |
SSS |
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Hint |
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9. |
Based upon steps 1-5, what is the best conclusion you can make for step 6? . Given: ABCD is a rectangle with diagonals
 and 
Prove:  |
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A. |
 ; AAS |
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B. |
 and  are right triangles; Definition of a right triangle |
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C. |
 and  are right triangles; Definition of a right triangle |
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D. |
 ; SAS |
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Hint |
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10. |
If the seventh and final statement of the proof is , what reason can you give for making that statement? Given: ABCD is a rectangle with diagonals
and
Prove: |
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A. |
CPCTC |
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B. |
Hypotenuses of right triangles are congruent |
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C. |
SSS |
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D. |
Definition of diagonals of parallelograms |
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Hint |
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11. |
To prove that the diagonals of a rhombus are perpendicular bisectors of each other use _____. |
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A. |
either Slope or Midpoint Formula |
B. |
Slope Formula |
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C. |
both Slope and Midpoint Formula |
D. |
Midpoint Formula |
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Hint |
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12. |
Use the diagram below to write equations to prove that opposite sides of a parallelogram are congruent. |
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A. |
 and  |
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B. |
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C. |
 and  |
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D. |
 and  |
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Hint |
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