Points, Lines, and Planes
Overview
Geometry begins with three undefined terms — point, line, and plane — that are described rather than defined. From them we build segments, rays, and angles, and we describe how points, lines, and planes relate: points on the same line are collinear, points in the same plane are coplanar, and lines and planes meet at intersections. This lesson sets the vocabulary every later lesson depends on.
Vocabulary
- Point
- A specific location in space. A point has no dimension; it is represented by a dot and named with a capital letter.
- Line
- A series of points that follows a straight path and extends forever in both directions. A line has no thickness; it is named by a lowercase script letter or by any two points on it.
- Line Segment
- A section of a line with two defined endpoints. A segment is named by its two endpoints.
- Ray
- A part of a line that has one defined endpoint and extends forever in one direction. A ray is named by its endpoint followed by another point on the ray.
- Opposite Rays
- Two rays that share an endpoint and extend in opposite directions, together forming a line.
- Plane
- A flat surface that extends forever in all directions and has no thickness. A plane is named by a capital script letter or by any three noncollinear points in it.
- Collinear Points
- Points that lie on the same line. Any two points are collinear; the term describes a third point, or a group of points, in relation to a line.
- Coplanar
- Points or lines that lie in the same plane. Points or lines that do not all lie in one plane are noncoplanar.
Main Ideas
- Points, lines, and planes are the building blocks of geometry. A point has no size, a line has length but no thickness, and a plane is a flat surface with no thickness.
- Two points determine a line, and three noncollinear points determine a plane.
- Two lines intersect at exactly one point. Two planes intersect at a line. A line can intersect a plane at a single point.
- Segments have endpoints and can be measured; lines and rays extend forever and cannot be measured.
- A point lies on a line given by an equation exactly when its coordinates satisfy the equation — substituting the coordinates is how collinearity with a graphed line is tested.
Lesson Notes
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Lesson Video
Watch the lesson video.
Interactive Activity
Explore points, lines, and planes, name figures from a diagram, and find where figures intersect.
Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.