Line, Ray, and Line Segment
Understanding the building blocks of geometry
Introduction: The Plane
What is a Plane?
A plane is a flat surface that extends infinitely in all directions. Think of it like:
- The surface of a perfectly flat table (but going on forever)
- The surface of still water in a pond (but infinite)
- A sheet of paper that never ends
- A plane has no thickness — only length and width
- We can only draw or see a part of a plane (it's infinite!)
- Planes are labeled with lowercase Greek letters: plane α, plane β
A plane extends infinitely in all directions (arrows show it continues)
The Line (Прямая)
What is a Line?
A line is a perfectly straight path that extends infinitely in both directions.
Properties of a Line:
- No beginning, no end — it goes on forever in both directions
- Perfectly straight — no curves or bends
- Infinite length — cannot be measured
- No endpoints — just keeps going
- No thickness — we draw it thick so we can see it
Naming a Line:
Use a lowercase letter:
line l, line m, line n
Use two points on the line:
line AB, line CD
Line l passing through points A and B
Fundamental Property
Through any two distinct points, exactly ONE line can be drawn.
This is an axiom — a fundamental truth of geometry that we accept without proof.
If you have points A and B, there is only ONE line that passes through both of them!
Intersection of Lines
Two different lines can intersect at most at ONE point.
Why? If they intersected at two points, they would be the same line (by the property above)!
Parallel Lines
Parallel lines are two different lines on a plane that never intersect, no matter how far they are extended.
Notation: AB ∥ CD (read as "AB is parallel to CD")
Examples: Railroad tracks, opposite edges of a ruler
Positions of Two Lines on a Plane
Option 1
They intersect at exactly one point
✕Option 2
They are parallel (never intersect)
∥Option 3
They are the same line (coincide)
≡There are no other possibilities!