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Reasoning
On One Conditional...
Properties, Postulates, and Theorems...
Oh My!
Vocabulary
Prove That!
100
The process of reasoning that a rule or statement is true because specific cases are true
What is inductive reasoning?
100
The hypothesis and conclusion of: If the sun is shining then it is summer.
What is hypothesis: "the sun is shining" and conclusion: "it is summer"?
100
The property that justifies the statement "If m = n, then n = m"
What is the symmetric property of equality?
100
A statement believed to be true
What is a conjecture?
100
The reason for the first step of any proof
What is "Given"?
200
The process of using logic to draw conclusions
What is deductive reasoning?
200
The truth value of the following conditional statement (if false, state a counterexample): If a figure has four sides, then it is a square.
What is false -- a rectangle has four sides and is not a square?
200
The property that justifies the statement 56 = 56
What is the reflexive property of equality?
200
Statements that have the same truth value
What are logically equivalent statements?
200
The last statement in any proof will always be this
What is what you are asked to prove?
300
A counterexample that shows the following conjecture is false: If ∠A and ∠B are complementary, then ∠A and ∠B are not congruent
What is ∠A and ∠B measure 45° each?
300
The inverse of "If a four-sided figure is a square, then it is a rectangle" and its truth value
What is "If a four-sided figure is not a square, then it is not a rectangle" -- false?
300
The property that justifies the statement e = f and f = g so e = g
What is the transitive property?
300
A statement that describes a mathematical object and can be written as a true biconditional statement
What is a definition?
300
The missing reason in the following proof:
Statements Reasons
∠2 ≅ ∠3 Given
m∠2 = m∠3 ???
What is "definition of congruent angles"?
400
The validity of the following conjecture by the Law of Syllogism: Given: If you are in Philadelphia, then you are in Pennsylvania. If you are at the Franklin Institute, then you are in Philadelphia. Conjecture: If you are at the Franklin Institute, then you are in Pennsylvania.
What is the conjecture is valid?
400
"If an angle measures 90° then it is a right angle" written as a biconditional statement
What is "An angle measure 90° if and only if it is a right angle"?
400
The theorem that justifies the following: ∠R and ∠S are a linear pair, so ∠R and ∠S are supplementary
What is the linear pair theorem?
400
A statement that can be written in the form "if p, then q" where p is the hypothesis and q is the conclusion
What is a conditional statement?
400
The blanks in the following proof: Given: B is the midpoint of segment AC and segment AB ≅ segment EF. Prove: segment BC ≅ segment EF
Statements Reasons
B is the midpoint of segment AC Given
(a) definition of midpoint
segment AB ≅ segment EF Given
segment BC ≅ segment EF (b)
What are (a) segment AB ≅ segment BC and (b) transitive property of equality?
500
The next two numbers in the pattern 1, 1, 2, 3, 5...
What are 8 and 13?
500
The inverse, converse, and contrapositive and their truth values of: "If Ms. Bloom has the flu, then she stays home from school."
What is... Inverse: "If Ms. Bloom doesn't have the flu, then she doesn't stay home from school" - false Converse: "If Ms. Bloom stays home from school, then she has the flu" - false Contrapositive: If Ms. Bloom doesn't stay home from school then she doesn't have the flu" - true ???
500
The theorem that justifies the following: ∠T and ∠U are complementary and ∠T and ∠V are complementary, so ∠U ≅ ∠V
What is the congruent complements theorem?
500
An example that proves a conjecture or statement is false
What is a counterexample?
500
The blanks in the following proof: Given: ∠BAC is a right angle; ∠2 ≅ ∠3 Prove: ∠1 and ∠3 are complementary
Statements Reasons
∠BAC is a right angle Given
m∠BAC = 90° (a) ?
m∠1 + m∠2 = 90° Angle addition postulate
(b) ? Given
(c) ? Definition of congruent angles
m∠1 + m∠3 = 90° (d) ?
(e) ? Definition of complementary angles
What are... (a) Definition of right angles (b) ∠2 ≅ ∠3 (c) m∠2 = m∠3 (d) Substitution (e) ∠1 and ∠3 are complementary