Math Postulates, Properties, and Theorums

The Reflexive Property

*** A=A This property simply states that an item or number equals itself.

The Transitive Property

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

The Symmetric Property

*** If a=b, then b=a It's just the inverse of the same equation and how it is the same equation still.

The Congruent Supplements Theorem

If angle 1 and angle 2 are supplements, and angle 1 and angle 3 are supplements as well, then angle 2 and angle 3 are congruent.

The Substitution Property

If x=6, then you can replace any x's in an equation with 6.

The Congruent Compliments Theorem

Same as The Congruent Supplements Theorem, except with complimentary angles.

The Addition Property

Simply addition.

The Vertical Angle Theorem

Simply states that vertical angles are congruent.

The Subtraction Property

Simply the property of subtraction.

Definitions

Sometimes as a proof, you simply need to say it is the definition of a word. If line segment AC has a midpoint B, then a statement is that AB = BC and the proof would be "The definition of Midpoint."

Givens

The first statement of a two column proof will always be given, so the proof of the statement will simply be "Given."

The Area Addition Postulate

This postulate simply states part plus part equals the whole of an irregular shape.

The Segment Addition Postulate

This postulate states that a part of a line segment plus another part equals the whole length of the segment if there are no more additional parts.

The Angle Addition Postulate

This postulate states that a part of an angle plus another part of the same angle equals the whole angle if there are no more additional parts parts.

The Linear Pair Postulate

This postulate states that all linear pairs must be supplementary.

The Right Angle Theorem

This theorem doesn't have a name, so you would simply state "All right angles are congruent." Meaning, all right angles have the same measure.

Properties of Congruents or Equalities

Three of the properties, marked with stars, can be properties of Congruents or of Equalities. The three are the Transitive, the Symmetric, and the Reflexive Property. If an equation states that AB = BA, it uses the Symmetric Property of Equality, while if it was AB is congruent to BA, it would be the Symmetric Property of Congruent.