Geometry - Angle Classifiers, Properties, and Postulates

Adjacent angles

Two angles that lie in the same plane and have a common vertex and a common side, but no common interior points.

Linear pair

Two adjacent angles with noncommon sides that are opposite rays.

Vertical angles

Two nonadjacent angles formed by two intersecting lines.

Congruent angles

Angles that have the exact same measure in degrees.

Complementary angles

Two angles with measures that have a sum of 90 degrees.

Supplementary angles

Two angles with measures that have a sum of 180 degrees.

Perpendicular angles

Lines, segments, or rays that form right angles.

Undefined terms

Intuitive ideas that aren’t defined

Vertex

The meeting point of an angle.

Sides [of an angle]

The lines that make up an angle.

Angle addition postulate

“One part plus another part equals a whole“

Bisector [of an angle]

A ray, line, or segment that divides the angle into two congruent angles.

The word “exists“ means…

“There is at least one.“

The word “unique“ means…

“There is no more than one.“

The word “determine“ means…

“To establish exactly.“

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

Distributive Property

If a(b + c), then a(b + c) = ab + ac

Substitution Property

If a = b, then a may be replaced by b in any expression or equation.

Reflexive Property

For any real number, a = a

Symmetric Property

If a = b, then b = a

Transitive Property

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

CLT [Combine Like Terms]

a + a + b = 2a + b

What can be used as reasons when using the properties of equality?

Properties, definitions, postulates, and theorems.

In a two-column proof, the left side contains the…

Statements/steps

In a two-column proof, the right side contains the…

Reasons