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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

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

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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
Defined Terms: Segments and Rays

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

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.

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.

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.