Theorems, Postulates, Properties, Definitions

Postulates

Angle Addition Postulate- If a point  is in the interior of an angle , then .

Segment Addition Postulate- If a point  is between points  and , then .

Corresponding Angles Postulate- If a transversal crosses two parallel lines, then the corresponding angles are congruent

Converse of the Corresponding Angles Postulate- If the corresponding angles are congruent, then the transversal crosses two parallel lines.

Definitions

Adjacent Angles- Two angles are adjacent if and only if they have a common vertex, share a common side, and have no common interior points

Congruent Angles- Two angles are congruent if and only if their measures are equal

Congruent Segments- Two segments are congruent if and only if their lengths are equal

Midpoint- A point is a midpoint if and only if it splits a segment into two congruent parts.

Segment bisector- A line, ray, or segment is a segment bisector if and only if it splits the segment into two congruent parts

Angle bisector- A line, ray, or line segment is an angle bisector if and only if it splits the angle into two congruent parts

Supplementary- Two angles are supplementary if and only if their measures add up to 180º

Complementary- Two angles are complementary if and only if their measures add up to 90º

Linear Pair- Two angles form a linear pair if and only if they are adjacent and their non-shared sides form opposite rays.

Theorems

Linear Pair Theorem- If two angles form a linear pair, then they are supplementary

Vertical Angles Theorem- If two angles are vertical angles, then they are congruent

Alternate Interior Angles Theorem- If a transversal crosses two parallel lines, then the alternate interior angles are congruent

Alternate Exterior Angles Theorem- If a transversal crosses two parallel lines, then the alternate exterior angles are congruent

Same Side Interior Angles Theorem- If a transversal crosses two parallel lines, then the same side interior angles are supplementary

Properties

Addition Property of Equality-  If , then

Subtraction Property of Equality-  If , then

Multiplication Property of Equality-  If , then

Division Property of Equality-  If  and , then .

Substitution Property of Equality- If , then  can be substituted for  in any expression.

Transitive Property of Equality-  If  and , then .  (If two things are equal to the same thing, then they are equal to each other)

Reflexive Property of Equality-     (Things are always equal to themselves)

Transitive Property of Congruence-  If  and , then .  (If two things are congruent to the same thing, then they are congruent to each other)

Reflexive Property of Congruence-     (Things are always congruent to themselves)

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