Download Name Date Pd. ______ D.6.2 and G.8.4 Logic and Reasoning Test

Name __________________________________ Date ___________________ Pd. __________
D.6.2 and G.8.4 Logic and Reasoning Test
____ 1. Identify the hypothesis and conclusion of this
conditional statement:
Two lines are perpendicular if they intersect at a
right angle.
6. Write the converse, inverse and contrapositive of
the following conditional statement. Determine the
truth value of all four statements. Explain or give a
counterexample to support each answer.
a. Hypothesis: The two lines are perpendicular.
Conclusion: Two lines intersect at right angles.
If you live in Daytona Beach, then you live in Florida.
Converse:
b. Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are perpendicular.
c. Hypothesis: The two lines are not perpendicular.
Conclusion: Two lines intersect at right angles.
d. Hypothesis: Two lines intersect at right angles.
Conclusion: The two lines are not perpendicular.
Inverse:
Contrapositive:
____ 2. What is a counterexample for the conjecture?
Conjecture: The product of two positive numbers is
greater than the sum of the two numbers.
____ 7. What is the converse of the following
conditional?
If a point is in the first quadrant, then its coordinates
are positive.
a. 3 and 5
b. 2 and 2
c. A counterexample exists, but it is not shown above.
d. There is no counterexample. The conjecture is true.
____ 3. The Transitive Property of Congruence states:
If
______.
a.
b.
c.
d.
a. If a point is in the first quadrant, then its coordinates
are positive.
b. If a point is not in the first quadrant, then the
coordinates of the point are not positive.
c. If the coordinates of a point are positive, then the
point is in the first quadrant.
d. If the coordinates of a point are not positive, then the
point is not in the first quadrant.
____ 4. Name the Property of Congruence that
justifies the statement:
If
.
a. Symmetric Property
b. Transitive Property
c. Reflexive Property
d. none of these
5. Find the truth value of the following statement.
Explain or give a counterexample to support your
answer.
All animals have fur.
____ 8. Which conditional has the same truth value as
its converse?
a. If two lines are parallel, then they are not skew.
b. If a figure is a square, then it has four sides.
c. If x – 17 = 4, then x = 21.
d. If an angle has a measure of 80, then it is acute.
____ 9. Determine whether the conditional and its
converse are both true. If both are true,
combine them as a biconditional. If either is
false, give a counterexample.
12. What are the converse, inverse, and contrapositive
of the following true conditional?
If a figure is a rectangle, then it is a parallelogram.
If an angle is a right angle, its measure is 90.
If an angle measure is 90, the angle is a right angle.
Converse:
a. One statement is false. If an angle measure is 90, the
angle may be a vertical angle.
Inverse:
b. One statement is false. If an angle is a right angle, its
measure may be 180.
c. Both statements are true. An angle is a right angle if
and only if its measure is 90.
Contrapositive:
d. Both statements are true. The measure of angle is 90
if and only if it is not an acute angle.
____ 10. Is the statement a good definition? If not, find
a counterexample.
If angles are a linear pair, then they are
supplementary.
a. The statement is a good definition.
13. Using the law of detachment and the law of
syllogism, what conclusion can you make, if any,
from the following statements?
If you score an 89% or lower on a test, then you can
retake it.
You scored an 82% on a test.
b. No; nonadjacent angles measuring 60 and 30 are a
counterexample.
c. No; nonadjacent angles measuring 20 and 160 are a
counterexample.
d. No; the counterexample is not listed above.
____ 11. Which biconditional is NOT a good
definition?
a. A whole number is odd if and only if the number is
not divisible by 2.
b. An angle is straight if and only if its measure is 180.
c. A whole number is even if and only if it is divisible
by 2.
d. A ray is a bisector of an angle if and only if it splits
the angle into two angles.
14. Using the law of detachment and the law of
syllogism, what conclusion can you make, if any,
from the following statements?
If two angle measures sum to 180, then the angles are
supplementary.
If two angle measures sum to 90, then the angles are
complementary.
____ 15. Complete the two-column proof.
Given:
Prove:
a. a. Given
c. a. Given
b. Addition Property of Equality
b. Addition Property of Equality
c. Division Property of Equality
c. Multiplication Property of Equality
b. a. Given
d. a. Given
b. Subtraction Property of Equality
b. Subtraction Property of Equality
c. Multiplication Property of Equality
c. Division Property of Equality
____ 16. Given:
Prove: x = 45
P
,
, and
.
R
Q
S
Drawing not to scale
,
, and
x + 7 + x + 3 = 100
2x + 10 = 100
2x = 90
x = 45
a. Given
b. __________
c. Substitution Property
d. Simplify
e. __________
f. Division Property of Equality
a. b. Angle Addition Postulate; e. Addition Property of Equality
b. b. Angle Addition Postulate; e. Subtraction Property of Equality
c. b. Protractor Postulate; e. Addition Property of Equality
d. b. Protractor Postulate; e. Subtraction Property of Equality
____ 17. Given: mAEB = 7x – 8 and mDEC = 6x + 11
Prove: x = 19
mAEB = 7x – 8 and mDEC = 6x + 11
Given
a. ___________________________
Vertical angles are congruent
b. ___________________________
Substitution Property
x – 8 = 11
x = 19
a. a. mAED = mBEC; b. 7x – 8 = 6x + 11
b. a. mAEB = mDEC; b. 7x – 8 = 6x + 11
c. a. mAED = mBEC; b. 7x – 8 + 6x + 11 = 180
d. a. mAEB = mDEC; b. 7x – 8 + 6x + 11 = 180
Subtraction Property of Equality
Addition Property of Equality