Conditional / Converse
Contrapositive / Inverse
Inductive vs. Deductive
Algebraic Proof
Geometric Proof
100
Write this as a conditional statement: Tenth graders are in Geometry.
If you are a tenth grader, then you are in Geometry.
100
Write the Inverse:
If you like tennis, then you play on the tennis team.
If you don't like tennis, then you don't play on the tennis team.
100
Is the following inductive or deductive reasoning?
All invertebrates do not have a spine.
Starfish are invertebrates. Therefore, starfish don't have a spine.
Deductive Reasoning
(Law of Detachment)
100
What algebraic property belongs in the blank for step 2?
The Distribution Property
100
Use the diagram to write a valid geometric conclusion.
Any of these count:
angle c = 133 -or- angle a = 133
angle b = 47
(others work, too. Angle addition postulate, for example.)
200
Write the contrapositive of: "If it is a puppy, then it is small."
"If it is not a puppy, then it is not small."
200
Write the inverse:
If x is not odd, then 2x is even.
"If x is odd, then 2x is not even.
200
Is the following inductive or deductive reasoning? Jennifer leaves for school at 7 am and is on time. Therefore, if Jennifer leaves for school after 7 am tomorrow she will be late.
Inductive Reasoning
200
Complete the proof:
2.) Distribution
3.) Subtraction Property of =
4.) Subtraction Property of =
5.) Division Property of =
6.) Symmetric Property
200
Use the diagram to write a valid geometric conclusion.
Answers may vary.
examples;
Angles BXC and CXD = 90
Angles AXD and BXC are congruent
300
Write as a conditional statement AND its converse: A line contains at least 2 points.
"If it is a line, then it contains at least 2 points." AND "If it contains at least 2 points, then it is a line."
300
Write the contrapositive:
If n doesn't have more than 2 factors, then n is prime.
If n is not prime, then n has more than 2 factors.
300
What is the law of syllogism?
Deductive reasoning in which you 'chain' statements together to form a conclusion
300
Given: -6n = 48
Prove that n = -8
1.) Given
2.) Division Property of Equality
300
What can be concluded from the statement:
m<1 + m<2 = 180
Angle 1 and angle 2 are supplementary
400
Can the following be written as a biconditional statement? "If it is raining, then clouds are in the sky."
No, because the converse is False.
400
Write the contrapositive of the statement, and then decide the truth value of the original statement and its contrapositive:
"If x is even, then x + 1 is odd."
CONTRAPOSITIVE: "If x + 1 is not odd, then x is not even."
Both are true.
400
a.) Create a conclusion from the given statements:
The Boulevard Diner always serves apple pie with vanilla ice cream.
You order apple pie.
b.) Was your reasoning inductive or deductive?
Conclusion; I will get vanilla ice cream.
Deductive Reasoning
400
Given: 3(n + 1) = -6
Prove: n = -3
1.) Given
2.) 3n + 3 = -6 Distributive Property
3.) 3n = -9 Subtraction Property of =
4.) n = -3 Division Property of =
400
complete the skeleton proof
500
Create an example of a statement that can be written biconditionally.
Example;
2n + 1 is odd if and only if n is an integer.
500
How are the inverse and the contrapositive related to each other?
Inverse: ~p --> ~q
Contrapositive: ~q --> ~p
The contrapositive is the converse of the inverse.
500
Sparzak drank 12 gallons of chocolate milk in the last 3 weeks.
In the following week, he will drink 4 gallons of chocolate milk.
Is this reasoning inductive or deductive?
Inductive Reasoning
500
Given: 3(4x - 1) - 2x = -43
Prove: x = -4
1.) Given
2.) 12x - 3 - 2x = -43 Distribution
3.) 10x - 3 = -43 Combine Like Terms
4.) 10x = -40 Addition Property of =
5.) x = -4 Division Property of =
500
Write a proof with the information in the image as given.
Prove; ∠PTR ≅ ∠QTS
Answers vary. Example:
1.) ∠PTQ ≅ ∠RTS
Given
2.) m∠1 = m∠2
Definition of Congruence
3.) m∠1 + m∠2 = m∠3 + m∠2
Addition Property of =
4.) m∠PTR = m∠1 + m∠2
m∠QTS = m∠3 + m∠2 Angle Addition Postulate
5.) m∠PTR = m∠QTS
Substitution
6.) ∠PTR ≅ ∠QTS
Definition of Congruent