Undefined terms
Intuitive concepts not explicitly defined since they
define themselves. The 3 undefined terms are: point,
line, plane
Point
Location, without a size. Represented by a dot.
Line
Infinite number of points on a straight path
extending infinitely in two directions.
Plane
Infinite number of points on a flat surface extending
infinitely in three directions.
Segment
A finite piece of a line
Ray
A piece of a line that extends infinitely in only one
direction.
Opposite Rays
Two rays on the same line with the same endpoint and
extend in opposite directions.
Angle
Geometric figure formed by 2 rays with one common
endpoint.
Endpoint
the point(s) on the end of a segment or ray
Collinear points
Points all in one line (can draw a line through all of them
at once)
Postulate
True statement that is accepted without proof; used
as a basis to prove other things (synonym: axiom)
Segment Addition
Postulate
If points A, B, and C are collinear and B is between A &
C, then AB + BC = AC.
Acute angle
Measures between 0 and 90 degrees.
Right angle
Measures 90 degrees.
Obtuse angle
Measures between 90 and 180 degrees.
Straight angle
Measures 180 degrees.
Angle Addition
Postulate
If point B lies in the interior of ∠ AOC, then m ∠ AOB
+ m ∠ BOC = m ∠ AOC.
Congruent
Same shape, same size - Having the same
measurement or length.
Perpendicular
bisector of a
segment
A line, segment, or ray that is perpendicular to the
segment and divides the segment into two congruent
segments.
Angle bisector
A ray that divides an angle into two congruent angles.
Midpoint of a
segment
A point that divides the segment into 2 congruent
segments
𝑥
Midpoint Formula
Distance Formula
Inductive reasoning
(Honors Only)
2
𝑑
𝑥
𝑥 𝑦
,
𝑥
𝑦
2
𝑦
𝑦
Reaching conclusions based on a pattern of specific
examples of past events
Deductive reasoning
Uses logical steps based on given facts to reach a
conclusion.
A counterexample
An example that proves a statement false.
Conditional
Statements
An “If-Then” statement with a hypothesis & conclusion
(if p, then q)
The converse of a
Exchange the hypothesis and the conclusion. (if q, then
conditional statement p)
The negation of a
Opposite meaning of the original statement. (not p)
conditional statement
The inverse of a
Negate both the hypothesis and the conclusion of a
conditional statement statement. If not p, then not q.
The contrapositive of
a conditional
statement
Biconditional
statement
Negate and reverse both the hypothesis and the
conclusion of a statement. If not q, then not p.
Addition Property
If a = b and c = d, then
a+c=b+d
Subtraction
Property
If a = b and c = d,
then a - c = b - d.
Multiplication
Property
Division Property
If a = b, then ca = cb.
The statement & its converse are both true. They
can be combined using the words if and only if.
If a = b and c ≠ 0, then a ÷ c = b ÷ c
Reflexive property
a=a
Symmetric Property If a = b, then b = a
Transitive Property
If a = b and b = c, then a = c
Substitution
Property
If a = b, then either a or b may be substituted
for the other in any equation (or inequality)
Distributive Property a (b + c) = ab + ac
Complementary
angles
Supplementary
angles
Linear pair
Angles whose measures add up to 90°.
Adjacent angles whose edges form a line.
Definition of
congruent angles
Angles are congruent iff their measurements are
equal.
Theorem
A statement that must be proven
Angles whose measures add up to 180°.
Definition of Midpoint If B is the midpoint of 𝐴𝐶 , then 𝐴𝐵 ≅ 𝐵𝐶 & AB = BC.
Definition of Angle
Bisector
If 𝐵𝐷⃗ bisects ∠ ABC, then ∠ ABD ≅ ∠ DBC and m ∠
ABD = m ∠ DBC.
Vertical Angle
Theorem
If 2 angles are vertical angles, then they are
congruent to each other (measurements are equal).
Linear Pair Theorem
If 2 angles form a linear pair, then they are
supplementary to each other.