Geometry / Unit 1: Foundations of Geometry
1.1 Points, Lines and Planes
Notes
Geometry starts with three undefined terms: point, line and plane. We describe them instead of defining them.
- A point is a location with no size. Name it with a capital letter, like $A$.
- A line is straight, has no thickness and goes on forever both ways. Name it with two points, $\overleftrightarrow{AB}$, or a lowercase letter.
- A plane is a flat surface that goes on forever. Name it with three points not on one line, or a capital script letter.
- Collinear points lie on the same line. Coplanar points lie in the same plane.
- Two points determine exactly one line. Three noncollinear points determine exactly one plane.
- Two lines intersect in a point. Two planes intersect in a line.
- Example: points $A$, $B$ and $C$ are on line $m$, so they are collinear and also coplanar.
Practice
How many lines can be drawn through two different points?
Two points determine exactly one line.
Two different planes intersect. What is their intersection?
The intersection of two planes is a line, like where a wall meets the floor.
Points $P$, $Q$ and $R$ are not on the same line. Which statement is true?
Three noncollinear points determine exactly one plane.
Ready for more? Take the Unit 1 test.