Geometry/Chapter 1/Lesson 1

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In geometry, the words, point, line, and plane are undefined terms. These words do not have formal definition, but there is agreement about what they mean.

Key Concept
Football field.jpg

Undefined Terms

Point A point has no dimension. It is represented by a dot.

    • Points can be named like: Point A, Point B, etc.

Line A line has one dimension. It is represented by a line with two arrowheads, but it extends without end.

    • Through any two points, there is exactly one line. You can use any two points on a line to name it.

Plane A Plane has two dimensions. It is represented by a shape that looks like a floor or a wall, but it extends without end.

    • Through any three points not on the same line, there is exactly one plane. You can use three points that are not all on the same line to name a plane.

Football Field: The dots on the football field can be seen as a point. The lines on the football field can be seen as the geometric undefined term, line, and the football field itself can be interpreted as a plane.

Collinear points are points that lie on the same line. Coplanar points are points that lie in the same plane.

Example 1 Name points, lines, and planes[edit | edit source]

Wikiversity Geometry Lesson 1 (Identify Points, Lines, and Planes) p01.png

1 Give two other names for line PQ and for plane R.

PQ=

,

R=

,

2 Name three points that are collinear.

,

,

3 Name four points that are coplanar.

,

,

,


DEFINED TERMS In geometry terms that can be described using known words such as point or line are called defined terms.

Key Concept
Line AB.png
Defined Terms: Segments and Rays

Line AB and points A and B are used here to define the terms below.

Segm AB.png

Segment The line segment AB, or segment AB, consists of endpoints A and B and all points on line AB that are between A and B. Note that line AB can also be named line BA.

Rays AB.png

Ray The ray AB consists of the endpoint A and all points on line AB that lie on the same side of A as B. Note that ray AB and ray BA are different rays, since the vertex, or endpoint, is the first letter in naming a ray.

GeometryTextbookOppositeRaysPicCAandCB.PNG

Opposite Ray - If C is in between A and B, then CA and CB are opposite rays. Opposite rays are two rays that have the same endpoint, but go in different directions.

Segments/rays are collinear if they lie on the same line. Opposite rays are collinear as well. Lines, segments, and rays are coplanar if they lie in the same plane.