Unit 2 Vocabulary Flashcards

Conditional Statement

Conditional Statement

A logical statement that has two parts, a hypothesis (p) and a conclusion (q)

Negation

The opposite of the original statement

Converse

To exchange the hypothesis and the conclusion of a conditional statement

Inverse

To negate both the hypothesis and conclusion of a conditional statement

Contrapositive

To write the converse of a conditional statement then negate both the hypothesis and conclusion

Perpendicular Lines

It two lines form a right angle then they are perpendicular

Biconditional Statement

A statement that contains the phrase "if and only if"

Conjecture

An unproven statement that is based on observations

Inductive Reasoning

(B on observations) when you find a pattern in specific cases and then write a conjecture for the general case

Counterexample

A specific case for which the conjecture is false

Deductive Reasoning

Uses facts, definitions, accepted properties, and the laws of logic to form a logical argument

Law of Detachment

If the hypothesis of a true conditional statement is true, then the conclusion is also true

Law of Syllogism

If hypothesis p, then conclusion q

If hypothesis q, then conclusion r

If hypothesis p, then conclusion r

Two Point Postulate

Through any two points there exists exactly one line

Line-Point Postulate

A line contains at least two points

Line Intersection Postulate

If two lines intersect, then their intersection is exactly one point

Three Point Postulate

Through any three non-collinear points there exists exactly one plane

Plane-Point Postulate

A plane contains at least three non-collinear points

Plane-Line Postulate

If two points lie in a plane, then the line containing them lies in the plane

Plane Intersection Postulate

If two planes intersect, then their intersection is a line.

Addition Property of Equality

If a=b, then a+c=b+c

Subtraction Property of Equality

If a=b, then a-c=b-c

Multiplication Property of Equality

If a=b, then ac=bc

Division Property of Equality

If a = b, then a/c = b/c

Substitution Property of Equality

If a=b, then a can be substituted for b in any equation or expression (or b for a) in any equation or expression

Distributive Property of Equality

a(b+c)=ab+ac

Reflexive Property of Equality

a=a, AB=AB, m<A=m<A

Symmetric Property of Equality

If a=b, then b=a/If AB=CD, then CD=AB/If m∠A=m∠B, then m∠B=m∠A

Transitive Property of Equality

If a=b and b=c, then a=c, if AB=CD and CD=EF, then AB=EF

Proof

A logical argument that uses deductive reasoning to show that a statement is true

Two-column proof

A proof that has numbered statements and corresponding reasons that show an argument in a logical order.

Theorem

A statement that can be proven

Flowchart proof/flow proof

A proof format which uses boxes and arrows to show the flow of a logical statement

Right Angles Congruence Theorem

All right angles are congruent

Congruent Supplements Theorem

If two angles are supplementary to the same angle (or to congruent angles), then they are congruent

Congruent Complements Theorem

If two angles are complementary to the same angle (or to congruent angles), then they are congruent

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Vertical Angles Congruence Theorem

Vertical angles are congruent

Paragraph proof

A proof format which presents the statements and reasons of a proof as sentences