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 in about 99% of proofs
What is "Given"?
200
If Mike is in school then he is in Math class. Give a counterexample if false.
What is Mike could be in be in theology class?
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
Two angles are _____ if they have the same measure
What is congruent?
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 point on a line segment that divides the segment into two congruent parts
What is a definition of midpoint?
300
The missing reason in the following proof:
Statements Reasons
∠2 ≅ ∠3 Given
m∠2 = m∠3 ???
What is "definition of congruent angles"?
400
Use inductive reasoning to find the next two terms. -5, 3, -2, 1, 0, ___, ____
What is -1, 2?
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
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