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2.1 Patterns and Inductive Reasoning
2.2 Conditional Statements
2.3 Biconditionals and Definitiions
2.4 Deductive Reasoning
2.5/2.6 Reasoning in Algebra and Geometry/Prove Angle Congruent
100
Find the next two term in the sequence provided 1000, 100, 10
What is 1, 0.1
100
Rewrite each statement as a conditional statement All motorcyclists wear helmets
What is If a person is a motorcyclist, then that person wears a helmet.
100
Determine if the definition is a good definition if not explain: A newspaper has articles you read
What is No it is not a good definition because it is not reversible. Counterexample: A magazine
100
Use the Law of Detachment or Law of Syllogism to make a conclusion: If you practice tennis everyday, then you will become a better player. Colin practices tennis every day.
What is Colin will become a better player
100
Name the property of equality or congruence that justifies the last step written 2x+1=7 2x=6
What is Subtraction Property
200
What is the next two term of the sequence 34, 27, 20, 13, ...
What is 6, 1
200
Rewrite each statement as a conditional statement Two nonparallel lines intersect at one point
What is If two nonparallel lines intersect, then they intersect at one point
200
Determine whether the definition is a good definition if not explain A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays
What is YES it is a good definition because it is reversible
200
Use the Law of Detachment or Law of Syllogism to make a conclusion: <1 and <2 are supplementary. If two angles are supplementary, then the sum of their measures is 180
What is <1+<2=180
200
Name the property of equality or congruence that justifies the last step written 5x=20 x=4
What is Division Property
300
Find the next two terms in the sequence 6, 24, 96, 384, ...
What is 1536, 6144
300
Write the Converse of the conditional and determine if it is true or false. If false give a counterexample: If you play the tuba, then you play an instrument
What is If you play an instrument, then you play the tuba. (FALSE, you could play any other instrument (drum))
300
Determine if the definition is a good definition If not explain: An angle is a geometric figure
What is NOT a good definition because its not reversible (counterexample: a line is also a geometric figure)
300
Use the Law of Detachment or 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.
What is If two angles are vertical, then their measures are equal.
300
Name the property of equality or congruence that justifies the last step written m
What is Symmetric Property
400
Find a counter example to show that the conjecture is false The product of any integer and 2 is greater than 2
What is Sample Answer: -1 x 2 = -2 and -2 is not greater than 2 (multiplying by a negative or a fraction)
400
Write the Inverse of the conditional and determine if it is true or false. If false give a counterexample: If you play the tuba, then you play an instument
What is If you do not play the tuba, then you do not play an instrument (FALSE, you could play the drums (any instrument) and play an instrument)
400
Write the following as biconditional: An oxymoron is a phrase that contains contradictory terms.
What is A phrase is an oxymoron if and only if it contains contradictory terms
400
Use the Law of Detachment or 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
What is If your father buys new gardening gloves, then he will plant tomatoes
400
Name the property of equality or congruence that that is modeled here: AB = CD, CD = EF. Therefore, AB = EF
What is Transitive Property
500
find a counterexample to show that each conjecture is false The city Des Moines is in Iowa
What is (any other city in Iowa ex: Council Bluffs)
500
Write the Contrapositive of the conditional and determine if it is true or false. If false give a counterexample: If you play the tuba, then you play an instument
What is If you do not play an instrument, then you do not play the tuba (TRUE)
500
Write the following biconditional as two statements, a conditional and its converse: Two angles are complementary if and only if the sum of their measures is 90
What is Conditional: If two angles are complementary, then the sum of their measures is 90 Converse: If the sum of the measures of two angles is 90, the the angles are complementary
500
Use the Law of Detachment or Law of Syllogism to make a conclusion: If you live in Fairbanks, then you live in Alaska. If you live in Alaska, then you live in the largest state in the United States. Allan lives in Fairbanks.
What is Allan lives in Alaska
500
Name the property of equality or congruence that is modeled here: <A=<A
What is Reflexive