math properties

Addition property of Equality

Adding the same number to both sides of the equation, keeping the equation equal.

Distributive property

Multiplying a single term and two more terms inside a set of parenthesis, or adding together two terms with a variable

Substitution property

If x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation.

Properties of opposites

Adding a number to its opposite to create a zero

Identity of Addition

The sum of any number and zero is the original number

Identity of Multiplication

Any number multiplied by one is that original number

Reflexive property

For every real number x, x = x

A number equals itself

Symmetric property

For all real numbers x and y, if x = y then y = x

Transitive property

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

Midpoint Theorem

If M is the midpoint of AB, then AM is congruent to MB

Definition of bisect

Divides into two congruent parts

Supplement Theorem

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

Definition of congruent segments

if segment AB is congruent to segment CD, then AB = CD

Definition of congruent angles

If two angles are congruent they have the same measure

Definition of perpendicular lines

Two lines that meet at a right angle (90 degrees)

Definition of right angle

An angle measuring at 90 degrees

Definition of complementary angles

Two angles whose sum is 90 degrees

Definition of supplementary angles

Two angles whose sum is 180 degrees

Segment addition postulate

Given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC

Angle addition postulate

Two angles side by side with the same vertices creates a new angle whose measure equals the sum of the two original angles

Right angle Theorem

Perpendicular lines intersect to form 4 right angles.

All right angles are congruent.

Vertical angle Theorem

Vertical angles are always congruent