Inductive Reasoning
Find the pattern for the sequence. Use the pattern to show the next two terms.
15, 12, 9, 6, ...
Pattern: Subtracting 3
Next Two Terms: 3, 0
State the conditional statement for the following events.
p: My cat is on fire.
q: I will grab a fire extinguisher.
If my cat is on fire, then I will grab a fire extinguisher.
What is the symbolic form of a biconditional statement.
p <-> q
Describe the Law of Detachment. You can use words or symbolic symbols.
If the conditional is true, then p and q have to be true.
If p -> q is true, then p and q is true.
State the property that is displayed below.
AB⩭AB
Reflexive Property
What conjecture can you make about the 42nd term?
A, B, C, A, B, C, A, B, ...
C
State a counterexample to the following conjecture.
"If I love to eat bacon for breakfast, then everyone loves to eat bacon for breakfast!"
(Answer can vary)
Possible Answers: Someone is vegan, someone cannot eat pork, etc.
Which of the following is a good definition?
a. A fish is an animal that swims
b. Rectangles have four corners
c. Giraffes are animals with very long necks
d. A penny is a coin worth one cent
D. (The only statement that is reversible, precise, and well-defined)
What can you conclude about the following information?
If you are a senior, then you are planning to graduate in 2025.
Chase is a freshman.
No conclusion
What property was used to get from statement 1 to statement 2.
1. 3x-5=7
2. 3x=12
Addition Property
State a counterexample for the following conjecture.
The product of any integer and 2 is greater than 2.
An integer that is <1.
Rewrite the sentence as a conditional statement.
All gymnasts are good at balancing.
If a person is a gymnast, then they are good at balancing.
What two statements need to be true to form a true biconditional statement?
Conditional Statement (p->q) & Converse Statement (q->p)
What two things must be true in order to apply the Law of Syllogism?
1. All conditional statements in question must be true.
2. Corresponding statements must share an event (one that begins in the sentence and one that ends in the other sentence.)
State the property demonstrated below.
If A⩭B, B⩭C, then A⩭C
Transitive Property of Congruence
Use inductive reasoning to identify the next figure.
Triangle, Square, Pentagon, Hexagon, Septagon, ...
Octagon
Write the contrapositive of the following statement.
If I love to eat ice cream, then I am not lactose intolerant.
If I am lactose intolerant, then I do not love to eat ice cream.
State the biconditional with the following events.
p: A Disney princess is pretty.
q: A Princess is kind and selfless.
A Disney princess is pretty if and only if they are kind and selfless
What can be concluded with the following information.
If I want to win Jeopardy, then I will need to win points.
If I win points, then I know how to answer questions about math.
If I know how to answer questions about math, then I will do well on the math test.
Sophia wants to win Jeopardy.
Sophia will do well on the math test.
What property was used to go from statement 1 to statement 2.
1. Line Segment DE+ Line segment EF
2. Line Segment DF
Segment Addition Postulate
What conjecture can you make about the sum of the first 10 odd numbers?
Sum=1^2 + 2^2 +...+10^2
Sum = 385
What is the inverse for the following statement.
If I hate to carry around change, then I will use my credit card.
If I do not hate to carry around change, then I will not use my credit card.
Write the following biconditional as two statements, A conditional and its converse.
Two angles are supplementary if and only if the sum of their measures is 180.
Conditional: If two angles are supplementary, then the sum of their measures is 180.
Converse: If the sum of the measurements of two angles is 180, then the two angles are supplementary.
All of the following statements are true. State the final conclusion for the following statements.
p -> q
q -> r
k -> r
r -> d
q -> f
d -> q
p -> f
Will in the reasons for each step of this proof.
1. C is the midpoint of AD ____________________
2. AC⩭CD ____________________
3.AC=CD ____________________
4. 4x=2x+12 ____________________
5. 2x=12 ____________________
6. x=6 ____________________
1. Given
2. Def. of Segment midpoints
3. Def. of Congruent Line Segments
4. Substitution
5. Subtraction Property
6. Division Property