Geometry Honors (Tucker) Definitions, POEs, POCs, Postulates, and Theorems

Reflexive POC/POE

ex. ___ AB is congruent/equal to ___ AB

Symmetric POC/POE

ex. if ___AB = ___CD, then ___CD = ___AB

Transitive POC/POE

ex. if ___AB = ___CD and ___CD = ___EF, then ___AB = ___EF

Right Angle Congruence Theorem

All right angles are congruent

Congruent Supplements Theorem

If two angles are supplementary to the same angle, then they are congruent.

Congruent Complements Theorem

If two angles are complementary to the same angle, then they are congruent.

Linear Pair Postulate

If two angles share a linear pair, then they are supplementary.

Vertical Angles Congruence Theorem

Vertical angles are congruent.

Definition of Congruence

Two segments/ angles are congruent if they have equal length or measure

Definition of Midpoint

The midpoint of a segment divides the segment into two equal or congruent parts

Definition of Segment Bisector

A line, segment, or ray that divides a segment into two equal parts.

Definition of Angle Bisector

A line or ray that divides an angle into two equal parts.

Definition of Perpendicular Lines

Two lines that intersect to form two pairs of right angles

Definition of Parallel Lines

Two lines in the same plane that do not intersect

Definition of a Right Angle

An angle that measures exactly 90 degrees

Definition of Complementary Angles

Two angles whose measures add up to 90 degrees

Definition of Supplementary Angles

Two angles whose measures add up to 180 degrees

Segment Addition Postulate

If B is between A and C, then AB+BC = AC

Angles Addition Postulate

If point D is the interior of angles ABC, then angle ABD + angle DBC = angle ABC

Distributive Property

a(b+c) = ab+ac

Substitution POC/POE

If a=b, then b can replace a in any expression

Segment Congruence Postulate

Two segments are congruent if and only if they have the same measure

Angle Congruence Postulate

Two angles are congruent if and only if they have they have the same measure.