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1. |
Suppose p represents ''Abraham Lincoln was the sixteenth President.'' Which statement is the negation of P? |
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A. |
Abraham Lincoln was not the sixteenth President. |
B. |
Abraham Lincoln was not a President. |
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C. |
Abraham Lincoln was the fourteenth President. |
D. |
The sixteenth President was Abraham Lincoln. |
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2. |
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A. |
A triangle does not have three sides and February has 28 days. |
B. |
February does not have 28 days or a triangle has three sides. |
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C. |
February does not have 28 days and a triangle has three sides. |
D. |
A triangle does not have three sides or February has 28 days. |
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3. |
If it is raining, then Sue and Ian will not go to the football game is a true conditional, and it is raining. Use the Law of Detachment to reach a logical conclusion. |
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A. |
The football game will not be played in the rain. |
B. |
Sue and Ian will go to the football game. |
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C. |
Ian will go to the football game if Sue goes. |
D. |
Sue and Ian will not go to the football game. |
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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. |
If Eric prepares for the exam, then he will read the book. |
B. |
If Eric reads the book, then he will get a passing grade. |
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C. |
no logical conclusion. |
D. |
If Eric gets a passing grade, then he did prepare for the exam. |
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5. |
Which statement can be used to show that  if  is a median of  ? |
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A. |
The median of an isosceles triangle bisects the vertex angle. So, the segments opposite the angles are congruent. |
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B. |
 and  . Therefore, because corresponding parts of congruent angles are congruent. |
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C. |
The median of an isosceles triangle is a perpendicular bisector of the base. So, by definition of bisector, . |
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D. |
because  and  are reflections of each other. |
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6. |
Write a paragraph proof for the conjecture. If quadrilateral ABCD is an isoceles trapezoid, and  and  are diagonals, then  . |
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A. |
You know that quadrilateral ABCD is an isosceles trapezoid. That means that  because the legs of an isosceles trapezoid are congruent. Also,  because the base angles of an isosceles trapezoid are congruent. By the reflexive property,  . So,  by SAS. |
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B. |
You know that quadrilateral ABCD is an isosceles trapezoid. That means that  because the diagonals of an isosceles trapezoid are congruent. So, by SSS. |
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C. |
You know that quadrilateral ABCD is an isosceles trapezoid. That means that because the legs of an isosceles trapezoid are congruent. Also,  because the base angles of an isosceles trapezoid are congruent. By the reflexive property,  . So, by SAS. |
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D. |
You know that quadrilateral ABCD is an isosceles trapezoid.  by definition of a trapezoid. Also, because the legs of an isosceles trapezoid are congruent.  and  because they are alternate interior angles. So, by ASA. |
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7. |
Justify step 3 in the following proof.
Given: 
Prove:  |
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A. |
Angle Addition Postulate |
B. |
Transitive Property |
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C. |
Substitution Property |
D. |
Replacement Property |
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Hint |
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8. |
Using the figure QRST, what are the possible reasons for  ? |
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A. |
ASA |
B. |
All of these |
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C. |
SSS |
D. |
SAS |
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Hint |
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9. |
Write a statement and reason for step 3. Given: ABCD is a rectangle with diagonals
and
Prove: |
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A. |
; Opposite sides of a parallelogram are congruent |
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B. |
 is a right triangle; Definition of right triangle |
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C. |
 is a right angle; Definition of a rectangle |
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D. |
 ; Opposite sides of a parallelogram are parallel |
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10. |
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. |
 and  are right triangles; Definition of a right triangle |
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B. |
 ; SAS |
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C. |
 ; AAS |
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D. |
and  are right triangles; Definition of a right triangle |
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Hint |
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11. |
Which formula would you use to show that opposite sides of a quadrilateral are parallel using a coordinate proof? |
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A. |
Distance Formula |
B. |
Midpoint Formula |
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C. |
Slope Formula |
D. |
Pythagorean Theorem |
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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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