Vocabulary
Conditional Statements
Deductive Reasoning
Vertical Angles & Proofs
Miscellaneous
100
The part of a conditional that follows the "then" is called this.
What is the conclusion?
100
Rewrite the following sentence as a conditional statement:
School is closed on certain holidays.
What is, "If today is a certain holiday, then school is closed."
100
Define the Law of Detachment & the Law of Syllogism.
Detachment: If p --> q is true and p is true, then q is true.
Syllogism: If p --> q and q --> r are true, then p --> r is true.
100
Find the value of y in the diagram linked below.
What is y = 18?
100
Use the statements below to construct the compound statement: x V (y ^ z). Then determine its truth value.
x: Emperor penguins are black and white.
y: Polar bears are a threatened species.
z: Penguins wear tuxedos
Emperor penguins are black and white or polar bears are a threatened species and penguins wear tuxedos.
Truth Value: True
200
A conditional has a _________ of true or false.
What is truth value?
200
Write the converse of the following statement & determine its truth value:
If an angle is obtuse, then its measure is greater than 90 and less than 180.
What is, "If the measure of an angle is greater than 90 and less than 180, then the angle is obtuse."
Truth Value: TRUE
200
Us the Law of Detachment to make a conclusion:
If you practice tennis every day, then you will become a better player. Colin practices tennis every day.
Colin will become a better player.
200
What are the measures of <1, <2, and <3?
m<1 = 90
m<2 = 50
m<3 = 40
200
Make a conjecture about the pattern of this sequence and find the next term:
6, 24, 96, 384, . . .
What is multiply by 4 & 1536?
300
When a conditional & its converse are true, you can write them as a single true statement called this.
What is a biconditional?
300
Write the inverse of the following statement & determine its truth value:
If you play the tuba, then you play an instrument.
What is, "If you do not play the tuba, then you do not play an instrument."
Truth value: FALSE
300
Use the Law of Syllogism to make a conclusion.
If two angles are vertical, then they are congruent. If two angles are congruent, then their measures are equal.
If two angles are vertical, then their measures are equal.
300
Fill in the reason that justifies each step.
a. Given
b. Segment Add. Postulate
c. Substitution
d. Distributive Property
e. Subtraction
f. Divistion
300
What is the truth value of p ^ (~p V q) if p is false and q is true?
What is FALSE?
400
A statement that you prove true is called this.
What is a theorem?
400
Write the contrapositive of the following statement & determine its truth value:
If a figure is a square, then it has four sides.
What is, "If a figure does not have four sides, then it is not a square."
Truth Value: TRUE
400
Use the Law of Detachment to make a conclusion.
<1 and <2 are supplementary. If two angles are supplementary, then the sum of their measures is 180.
m<1 + m<2 = 180
400
Write a two-column proof for the following:
Given: 7(3k - 2) - 13k = 82
Prove: k = 12
Statement | Reason
1) 7(3k - 2) - 13k = 82 | 1) Given
2) 21k -14 - 13k = 82 | 2) Distributive Prop.
3) 8k - 14 = 82 | 3) CLT
4) 8k = 96 | 4) Addition
5) k = 12 | 5) Division
400
Name the operation that transforms
9a - 7a = 3a - 33 + 2a into 2a = 5a - 33, then find a.
What is combine like terms & a = 11?
500
The process of reasoning logically from given statements to a conclusion is called this.
What is deductive reasoning?
500
Write the converse, inverse, & contrapositive of the following statement & determine the truth values of each one:
If you are a teenager, then you are younger than 20.
What is...
Converse: If you are younger than 20, then you are a teenager. (FALSE)
Inverse: If you are not a teenager, then you are not younger than 20. (FALSE)
Contrapositive: If you are not younger than 20, then you are not a teenager. (TRUE)
500
Use the Law of Syllogism to make a conclusion.
If your father buys new gardening gloves, then he will work in his garden. If he works in his garden, then he will plant tomatoes.
If your grandfather buys new gardening gloves, then he will plant tomatoes.
500
Write a two-column proof.
Statement | Reason
1) <1 & <2 are | 1) Given
supplementary |
<3 & <2 are |
supplementary |
2) m<1 + m<2 = 180 | 2) Def. of Suppl. angles
m<3 + m<2 = 180 |
3) m<1 + m<2 = | 3) Transitive Prop. or
m<3 + m<2 | Substitution
4) m<1 = m<3 | 4) Subtraction
5) <1 is congr. to <3 | 5) Def. of congr. angles
500
Construct a truth table for ~q ^ (~p V q).