POINTS
LINES &
PLANES
The "Undefined Terms." These are the atoms of geometry. We cannot define them using simpler words; we can only describe them and build the universe upon them.
there is exactly one line.
Building Dimensions
Cuts of Infinity
A line goes on forever, but we can't build shapes with infinity. We must cut the line into pieces. These pieces are how we construct the universe.
Point
A location in space. It has no size, no width, no depth. It is represented by a dot.
Line
A straight path that extends infinitely in two directions. It has length, but no width.
Plane
A flat surface that extends infinitely in all directions. It has length and width, but no depth.
Collinear
Points that lie on the same line.
Line Segment
A part of a line bounded by two endpoints. It has a measurable length.
Ray
A part of a line that starts at an endpoint and extends infinitely in one direction.
Euclidean Axioms
Through any two points, there is exactly one line.
If two lines intersect, then they intersect in exactly one point.
If two planes intersect, then they intersect in exactly one line.