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Geometry Basics: Vocabulary

In elementary school you learn a lot of introductory geometric vocabulary. Now, you will be doing a LOT more with what you've learned. Let's do some review now, shall we?

The Basic Building Blocks: Undefined Terms

In geometry, the most basic figures are undefined; they cannot be defined by using a particular figure or shape. There are three of these terms: point, line, and plane.

point – names a specific location and has no size. It is represented by a dot.

Points are named with a capital letter.

 

line – a straight path that extends forever and has no thickness. It is represented by a line with an arrow at each end.

A line is named with a lower-case letter OR by two points (capital letters) on the line

 

plane – a flat surface that extends forever in all directions that has no thickness. It is represented by a script (italicized) capital letter.

Planes are named with a script/italicized capital letter OR three points that are NOT on a line.
 

collinear – points that lie on the same line

coplanar – points that lie in the same plane

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Defined Terms

Now, we can look at terms that are defined. These are probably what you remember from elementary school.

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segment (or line segment) – names a part of a line consisting of two points and all the points between. It is named by two endpoints.

Segments are named with by two endpoints (capital letters).

 

 

 

endpoint – a point at one end of a segment or the starting point of a ray. It is represented by a capital letter.

Endpoints are named with capital letters

 

 

 

ray – a part of a line that starts at an endpoint and extends forever in one direction as indicated by an arrow.

Rays are named with its endpoint and any other point on the ray (two capital letters).
 
 
 

opposite rays – two rays that share a common endpoint and form a line

 

 

 

 

angle – a figure formed by two rays with a common endpoint called a vertex.

Angles are named by the vertex. If that point is the vertex of more than one angle, three points are used to name the angle, with the middle point always naming the vertex.
 
*Note: When working with proofs, the term angle generally refers to angles formed by non-collinear rays unless otherwise stated.
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