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Deductive/Inductive Reasoning
Theorems
Properties
Random
Types of Statements
100
Would you use inductive or deductive reason to come to this conclusion: John was holding a fire extinguisher, so he must have been ready to put out a fire.
What is inductive.
100
Describe what a two-column proof is.
What is a proof where one column gives steps and statements that help solve the problem and a column next to it gives reasons such as theorems that justify each step.
100
What is the property shown here a(b+c) = ab + ac
What is Distributive property
100
What is the difference between deductive and inductive reasoning?
What is deductive reasoning uses definitely known facts to prove a definite answer where as inductive reasoning makes assumption and the conclusions are not 100% definite.
100
What is the truth value of a conditional statement?
What is: whether a statement is true or false
200
Complete this sequence: Washington, Adams, ?
What is Jefferson
200
Describe what the Vertical Angles Theorem?
What is a theorem that states that vertical angles are congruent.
200
Define the Symmetric Property
What is if a=b then b=a
200
Find a counter example for the following statement: When it rains, it pours.
What is it can rain lightly sometimes.
200
What is the inverse of a conditional statement
What is when you negate both the hypothesis and the conclusion of the conditional
300
Define the Law of Detachment
What is a law that states that if the hypothesis is true, than the conclusion is true
300
Describe what the Congruent Complements Theorem?
What is a theorem that says that if two angles are complements of the same angle, then they are congruent.
300
List the three properties of congruence
What is the reflexive property, symmetric property, and transitive property
300
Solve (2x + 30) + x = 180 and justify each step.
What is: 3x + 30 = 180 -> distributive property 3x = 150 -> subtraction property x = 50 -> division property
300
What is the converse of this statement:If the figure is a square, then the figure is a quadrilateral.
What is If the figure is a quadrilateral, then the figure is a square.
400
What can you determine from these facts. If a figure is a square , then the figure is a rectangle. If a figure is a rectangle, then the figure has four sides
What is if a figure is a square, then the figure has four sides.
400
Given that angle <1 = <4, prove that <2=<3
What is: 1. <1 = <4 -> given 2. <4 = <2 -> Vertical Angles Theorem 3. <1 = <2 -> Transitive Property 4. <1 = <3 -> Vertical Angles Theorem 5. <2 = <3 -> Transitive Property
400
Solve for 2x + 9 = 19 and justify the steps
What is: 1. subtract 9 from each side by the subtraction property 2. divide 2 by each side by the division property 3. x= 5
400
What properties make this equation true: 5/3=5/3
What is the division property and the reflexive property
400
Give the contrapositive of this statement: If m< a = 15 then
What is If
500
What can you conclude from the given informations: If you live in Accra, then you live in Ghanna. If you live in Ghanna, then you live in Africa, Aissa lives in Accra
What is Aissa lives in Africa
500
Given <1 and <3 are supplementary and <2 and <3 are supplementary, prove <1 = <2.
What is: 1. <1 and <3 are supplementary and <2 and <3 are supplementary -> given 2. m<2 + m<3 = 180 -> definition of supplementary angles 3. m<1 +m<3 = m<2 + m<3 -> transitive property 4. m<1=m<2 -> subtraction property 5. <1=<2 -> angles with the same measure are congruent
500
Given m<1 = m<3 prove m
What is: 1. m<1 = m<3 -> Given 2. m<2 = m<2 -> reflexive property 3. m<1 + m<2 = m<3 + m<2 -> addition property 4. m<1 + m<2 = m Angle Addition Postulate 5. m Substitution Property
500
Give the converse, inverse, and contrapositive of the following statement: If you are American citizen, then you have the right to vote.
What is: Converse: If you have the right to vote, then you are an American citizen. Inverse: If you are not an American citizen, then you don't have the right to vote Contrapositive: If you don't have the right to vote, then you aren't an American citizen.
500
Write a biconditional statement for the given A ray is an angle bisector and A ray divides an angle into two congruent angles.
What is A ray is an angle bisector if and only if it divides an angle into two congruent angles.