Proofs, Postulates, Theorems

A postulate is a statement that is assumed true without proof while a theorem is a true statement that can be proven.

A theorem is a statement that is assumed true without proof while a postulate is a true statement that can be proven.

They show you read the question.

They tell you what your end goal is.

They list what you know and are necessary to complete a proof.

Theorems

Given Statement(s)

Postulates

Reasons

Equality Property

Reflexive Property

Transitive Property

Associative Property

∠PQR = 38; B: Definition of Complementary Angles; C: Subtraction

Property of Equality

∠PQR = 38; B: Definition of Supplementary Angles; C: Reflexive Property

∠PQR = 38; B: Definition of Vertical Angles; C: Transitive Property

∠PQR = 38; B: Definition of Complementary Angles; C: Substitution

Vertical angle theorem

Subtraction property of equality

Transitive property of congruence

Definition of supplementary angles

Vertical angle theorem

Subtraction property of equality

Transitive property of congruence

Definition of supplementary angles

Vertical angle theorem

Subtraction property of equality

Transitive property of congruence

Definition of supplementary angles

Definition of Midpoint

Transitive Property

Addition Property

Segment Addition Postulate

Substitution Property

Given

Vertical Angles Theorem

Definition of Angle Bisector

Alternate Interior Angles Theorem