Review #2: Reasoning & Proofs

Flashcards covering vocabulary, inductive reasoning, conditional statements, and algebraic properties based on the provided review notes. These fill-in-the-blank flashcards are designed to help students prepare for their exam.

A statement you can prove and then use as a reason in later proofs is a(n) __.

theorem

__ is the process of using logic to draw conclusions from given facts, definitions, and properties.

Deductive reasoning

A(n) __ is a case in which a conjecture is not true.

counterexample

A statement you believe to be true based on inductive reasoning is called a(n) __.

conjecture

A statement where the conditional and converse are both true is called a __.

biconditional statement

The sum of an even number and an odd number is __.

odd

The square of any real number is __.

non-negative

The conjecture "If you have 25 cents then you have a quarter" is __.

True

The conjecture "If C is a midpoint of AB, then AC
≅ BC" is __.

True

The conjecture "If 2x + 3 = 15, then x = 6" is __.

True

The conjecture "There are 28 days in February" is __.

False

The conditional statement for "Parallel lines do not intersect" is "If lines are parallel, then they _.

do not intersect

The statement "If two angles are adjacent, then they have a common ray" is __.

True

The statement "If it is a weekday, then it is Monday" is __.

False

The truth value of the conditional statement "If m∠1 = 35°, then ∠1 is acute" is __.

True

The converse of "If m∠1 = 35°, then ∠1 is acute" is "If ∠1 is acute, then __."

m∠1 = 35°

The truth value of the converse "If ∠1 is acute, then m∠1 = 35°" is __.

False

The inverse of "If m∠1 = 35°, then ∠1 is acute" is "If m∠1 ≠ 35°, then __."

∠1 is not acute

The truth value of the inverse "If m∠1 ≠ 35°, then ∠1 is not acute" is __.

False

The contrapositive of "If m∠1 = 35°, then ∠1 is acute" is "If ∠1 is not acute, then __."

m∠1 ≠ 35°

The truth value of the contrapositive "If ∠1 is not acute, then m∠1 ≠ 35°" is __.

True

The truth value of the conditional statement "If ∠X is a right angle, then m∠X = 90°" is __.

True

The truth value of the converse "If m∠X = 90°, then ∠X is a right angle" is __.

True

The truth value of the inverse "If ∠X is not a right angle, then m∠X ≠ 90°" is __.

True

The truth value of the contrapositive "If m∠X ≠ 90°, then ∠X is not a right angle" is __.

True

A biconditional statement can be formed for "If ∠X is a right angle, then m∠X = 90°" because its conditional and converse are both __.

True

The biconditional statement for "If ∠X is a right angle, then m∠X = 90°" is "∠X is a right angle __ m∠X = 90°."

if and only if

The truth value of the conditional statement "If x is a whole number, then x = 2" is __.

False

The truth value of the converse "If x = 2, then x is a whole number" is __.

True

The truth value of the inverse "If x is not a whole number, then x ≠ 2" is __.

True

The truth value of the contrapositive "If x ≠ 2, then x is not a whole number" is __.

False

The property that justifies 𝑎 + 𝑏 = 𝑎 + 𝑏 is the __.

Reflexive Property of Equality

The property that justifies "If ∠RST
≅ ∠ABC, then ∠ABC
≅ ∠RST" is the __.

Symmetric Property of Congruence

The property that justifies "2x = y and y = 9, so 2x = 9" is the __.

Transitive Property of Equality

The property that justifies "(2 + 7) + 9 = 2 + (7 + 9)" is the __.

Associative Property of Addition

The property that justifies "If LM
≅ ST and ST
≅ YZ, then LM
≅ YZ" is the __.

Transitive Property of Congruence

The property that justifies "7(5) = 5(7)" is the __.

Commutative Property of Multiplication

The property that justifies "If a(b + 7) = 3 and a = 2, then 2(b + 7) = 3" is the __.

Substitution Property of Equality