Geometry Definitions and Theorems
Acute angle
Angle whose measure is greater than 0 but less than
90 degrees
Right angle
Angles whose measure is 90 degrees
Obtuse angle
Angle whose measure is greater than 90 but less than
180 degrees
Straight angle
Angle whose measure is 180 degrees
Congruent angles
Angles that have the same measure
Congruent segments
Segments that have the same length
Collinear
Points that lie on the same line
Noncollinear
Points that do not lie on the same line
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle
is always greater than the length of the third.
Theorem
A mathematical statement that can be proved
Thm - Right Angles
If two angles are right angles, then they are
congruent.
Thm - Straight Angles
If two angles are straight angles, then they are
congruent.
Segment bisector
A point, segment, ray, or line that divides a segment
into two congruent segments
Midpoint
The bisection point of a segment
Segment trisector
Two points, segments, rays, or lines that divide a
segment into three congruent segments
Trisection points
The two points at which the segment is divided into
three congruent segments
Angle bisector
A ray that divides an angle into two congruent angles
Angle trisector
Two rays that divide an angle into three congruent
angles
Postulate
An unproved assumption
Definition
Conditional Statement
States the meaning of a term or idea and is reversible
A statement in if-then form (p ==> q)
Hypothesis
The “if” part of a conditional statement
Conclusion
The “then” part of a conditional statement
Converse
q ==> p
Inverse
~p ==> ~q
Contrapositive
~q ==> ~p
Chain Rule
If p ==> q and q ==> r, then p ==> r
Probability
Perpendicular lines
Lines, rays, or segments that intersect at right angles
Complementary angles
Two angles whose sum is 90 degrees (a right angle)
Supplementary angles
Two angles whose sum is 180 degrees (a straight
angle)
Thm - Supplementary Angles
If angles are supplementary to the same angle, then
they are congruent.
Thm - Supplementary Angles
If angles are supplementary to congruent angles, then
they are congruent.
Thm - Complementary Angles
If angles are complementary to the same angle, then
they are congruent.
Thm - Complementary Angles
If angles are complementary to congruent angles,
then they are congruent.
Thm - Addition Property
If a segment is added to congruent segments, then
the sums are congruent.
Thm - Addition Property
If an angle is added to congruent angles, then the
sums are congruent.
Thm - Addition Property
If congruent segments are added to congruent
segments, then the sums are congruent.
Thm - Addition Property
If congruent angles are added to congruent angles,
then the sums are congruent.
Thm - Subtraction Property
If a segment (or angle) is subtracted from congruent
segments (or angles), then the differences are
congruent.
Thm - Subtraction Property
If congruent segments (or angles) are subtracted from
congruent segments (or angles), then the differences
are congruent.
Reflexive Property
An angle or segment is congruent to itself ( a).
Thm - Multiplication Property
If segments (or angles) are congruent, then their like
multiples are congruent.
Thm - Division Property
If segments (or angles) are congruent, then their like
divisions are congruent.
Thm - Transitive Property
If a  b and b  c, then a  c.
Opposite rays
Two collinear rays that have a common endpoint and
extend in different directions
Vertical angles
Two angles formed when the rays forming the sides
of one angle and the rays forming the sides of the
other angle are opposite rays.
Thm - Vertical Angles
Vertical angles are congruent.