1-7 Writing Proofs

Proofs

Uses given information and logical steps justified by definitions, postulates, theorems, and properties to reach a conclusion.

Conjecture

A conclusion reached by using inductive reasoning

A proof

A convincing argument that uses deductive reasoning. Can be written in many forms.

Inductive Reasoning

A type of reasoning that reaches conclusions based on a pattern of specific examples or past events.

Two-Column Proof

Statements and reasons are aligned into columns; One way to organize and present a proof.

Deductive Reasoning

A process of reasoning logically from given facts to a conclusion.

Flow Proof

Shows the logical connections between the statements.

Indirect Reasoning

A type of reasoning in which all possibilities are considered and then all but one are proved false.

Paragraph Proof

Shows the statements and reasons connected in sentences.

Theorem

A conjecture that is proven.

Coordinate Proof

A figure is drawn on a coordinate plane and the formulas for slope, midpoint, and distance are used to prove properties of the figure.

Linear Pair

A pair of adjacent angles whose noncommon sides are opposite rays.

Indirect Proof

Involves the use of indirect reasoning

Vertical Angles

Two angles whose sides form two pairs of opposite rays.

Congruent Figures

Has equal measures.

1-1

Vertical Angles Theorem; Vertical angles are congruent.

1-2

Congruent Supplements Theorem; If two angles are supplementary to congruent angles, or to the same angle, then they are congruent.

1-3

Congruent Complements Theorem; If two angles are complementary to congruent angles, or to the same angle, then they are congruent.

1-4

Right Angle Congruence Theorem; All right angles are congruent.

1-5

If two angles are congruent and supplementary, then each is a right angle.

1-6

Linear Pairs Theorem; The sum of the measures of a linear pair is 180.

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

Reflexive Property of Equality

a = a; b = b

Symmetric Property of Equality

If a = b, then b = a

Transitive Property of Equality

If a = b, and b = c, then a = c

Reflexive Property of Congruence

AB is congruent to AB; Angle A is congruent to Angle A.

Symmetric Property of Congruence

If AB is congruent to CD, then CD is congruent to AB; If Angle A is congruent to Angle B, then Angle B is congruent to Angle A.

Transitive Property of Congruence

If AB is congruent to CD, and CD is congruent to EF, then AB is congruent to EF; If Angle A is congruent to Angle B, and Angle B is congruent to Angle C, then Angle A is congruent to Angle C.