Geometry Vocab
Inductive reasoning
The process of reasoning that a rule or
statement is true because specific cases are true
Conjecture
A statement that is believed to be true
Expression
A mathematical phrase that contains operations,
numbers, and/or variables
Constant
A value that does not change
Difference
The result of subtraction
Function rule
An algebraic expression that defines a function
Rate of change
A ratio that compares the amount of change in
the dependent variable to the amount of change
in the independent variable
AKA: SLOPE
Variable
A symbol used to represent a quantity that can
change
Coefficient
A number multiplied by a variable
Formula
A literal equation that states a rule for a
relationship among quantities
Equation
A mathematical sentence that shows two
expressions are equivalent
Segment of a line
A part of a line consisting of two end points and
all points between them
Midpoint
The point that divides a segment into two
congruent segments
Congruent
Having the same size and shape, denoted by ≅
*objects and shapes use congruent
Equal
Having the same numeric value
*measurements and distances use equal
Bisect
To divide into two congruent parts
Proof
An argument that uses logic to show that a
conclusion is true
Postulate
A statement that is accepted as true without
proof. Also called an axiom.
Distance
The absolute value of the difference of the
coordinates of the points
*a measurement, numeric
Length
The distance between the two endpoints of a
segment
Construction
A method of creating a figure that is considered
to be mathematically precise. Figures may be
constructed by using a compass and
straightedge, geometry software, or paper
folding.
Intersect
To have one or more points in common
Conditional statement
A statement that can be written in the form “if
p, then q,” where p is the hypothesis and q is the
conclusion.
Hypothesis
The part of a conditional statement following
the word if.
Conclusion
The part of a conditional statement following
the word then.
Inverse operations
Operations that undo each other
Converse
The statement formed by exchanging the
hypothesis and the conclusion of a conditional
statement
Contrapositive
The statement formed by both exchanging and
negating the hypothesis and conclusion of a
conditional statement
Truth value
A statement can have a truth value of true or
false
Biconditional statement
A statement that can be written in the form “p if
and only if q.”
Counterexample
An example that proves that a conjecture or
statement is false
Negation
The negation of statement p is “not p,” written
as ∼ 𝑝.
Logically equivalent statements
Statements that have the same truth value
Deductive reasoning
The process of using logic to draw conclusions
Law of Syllogism
If a, then b.
If b, then c.
If a, then c.
a→b
b→c
a→c
Point
An undefined term in geometry, it names a
location and has no size.
Line
An undefined term in geometry , a line is a
straight path that has no thickness and extends
forever
Plane
An undefined term in geometry, a flat surface
that has no thickness and extends forever
Ray
An undefined term in geometry , a part of a line
that starts at an endpoint and extends forever in
one direction
Undefined term
A basic figure that is not defined in terms of
other figures.
*point, line, ray and plane
Endpoint
A point at an end of a segment or the starting
point of a ray.
Opposite rays
Two rays that have a common endpoint and
form a line
Collinear
Points that lie on the same line
Coplanar
Points that lie in the same plane
Non collinear
Points that do not lie on the same line
Non coplanar
Points that do not lie on the same plane
Vertex
Common point of two rays that form an angle.
measure
Size of an object (an angle or length)
Degrees
What we measure angles in
Side of an Angle
One of two rays that form an angle
Angle addition
The process of adding 2 angle measures
Angle bisector
A ray that divides an angle into two congruent
angles
Acute angle
An angle that measures greater than 0 and less
than 90 degrees
Right angle
An angle that measures 90 degrees
Obtuse
An angle that measures greater than 90 and less
that 180 degrees
Straight Angle
An angle formed by two opposite rays that
measures 180 degrees
Adjacent angles
Two angles in the same plane with a common
vertex and a common side, but no common
interior points
Non adjacent
two angles in the same plane that do not have a
common side
Interior of an angle
Between the two rays that form the angle
Exterior of an angle
Outside the two rays that form the angle
On an angle
On one of the 2 rays that form the angle
Protractor
Used to measure angles.
Supplementary angles
Two angles whose measures have a sum of 180
degrees
Complementary angles
Two angles whose measures have a sum of 90
degrees
Linear Pair
A pair of adjacent angles whose noncommon
sides are opposite rays
Vertical angles
The non adjacent angles formed by two
intersecting lines
Substitution
The process of exchanging two equal values with
in a problem
Addition Property of Equality
For real numbers a, b, and c, if a = b, then a + c =
b+c
*add the same value to each side
Subtraction Property of Equality
If a, b, and c are real numbers and a = b, then a
– c = b – c.
*subtract the same thing from each side
Angle Addition Postulate
If d is on the interior of / ABC,
then / ABD + / DBC = / ABC
Division Property of Equality
For real numbers a, b and c, where c ≠ 0, if a = b,
𝑎
𝑏
then = .
𝑐
𝑐
*divide all terms by the same value
Multiplication Property of Equality
If a, b, and c are real numbers and a = b, then
ac = bc
*multiply all terms by the same value
Definition
A statement that describes a mathematical
object and can be written as a true biconditional
statement.
Defn of Bisector
Use in a proof when concept of bisector is
introduced
Defn Straight Angle
Use in a proof when concept of straight angle is
introduced
Defn of Congruence
Use in a proof to state that two things are the
same size and shape
Defn of Equality
Use in a proof to state that two things are equal
in value
Transitive Property of Equality
a = b, and b = c, so a = c