Undefined Terms
This basic geometric idea has no size and marks a location.
Point
A part of a line that has two endpoints.
Line segment
This axiom states that any quantity is equal to itself.
Reflexive Axiom of Equality
This geometric concept extends infinitely in two directions with no thickness.
Line
A straight path that extends infinitely in one direction.
Ray
This axiom states that if one quantity equals a second, then the second equals the first.
Symmetric Axiom of Equality
This undefined term is a flat surface that extends infinitely in all directions.
Plane
Formed by two rays with a common endpoint.
Angle
This axiom states that if a first quantity equals a second and the second equals a third, then the first equals the third.
Transitive Axiom of Equality
These terms are considered the “building blocks” of geometric definitions.
Undefined Terms
Defined using points and rays, this measures how open or closed a figure is.
Angle measure
This property states that equal quantities may be substituted for one another in any expression.
Substitution Axiom of Equality
These three undefined terms form the foundation of Euclidean Geometry.
Point, line, and plane
Terms like midpoint and bisector belong to this classification.
Defined terms
This axiom states that multiplying the same number to both sides of an equation preserves equality.
Multiplication Axiom of Equality