Undefined & Defined Terms

Undefined & Defined Terms

Looking Back

A. Match the description to their correct figure.

Multiple Choice

Vertical Angles – are two angles opposite each other

Multiple Choice

Parallel Lines – lines on the same plane that do not intersect and always have the same distance from each other

Multiple Choice

Linear Pairs – two adjacent angles that form a line

Multiple Choice

Adjacent Angles – two angles that have a common side, a common vertex and no interior point in common

Multiple Choice

Perpendicular Lines – two lines that intersect at a right angle

Looking Back

B. Identify what is being described for each statement. Choose the correct answer.

Multiple Choice

An angle whose measure is 90°.

• Angle

• Collinear Points

• Line Segment

• Ray

• Right Angle

Multiple Choice

Points that lie on the same line.

• Angle

• Collinear Points

• Line Segment

• Ray

• Right Angle

Multiple Choice

A subset of a line with only one endpoint.

• Angle

• Collinear Points

• Line Segment

• Ray

• Right Angle

Multiple Choice

Two non-collinear rays that have a common endpoint called the vertex.

• Angle

• Collinear Points

• Line Segment

• Ray

• Right Angle

Multiple Choice

A portion of a line with two end points.

• Angle

• Collinear Points

• Line Segment

• Ray

• Right Angle

Brief Introduction

Undefined terms are terms that can be described but cannot be defined such as point, a line, and a plane. These terms can only be described intuitively. We imagine these geometric terms as they are difficult to replicate exactly in real life, but the idea of their image gives us a basis for all other terms. These terms are the basic building blocks of geometry.

Point

A point has no size, no length, no width, and no thickness. In geometry it only indicates location or position. It is named using a capital letter such as the one you noticed in a rectangular coordinate plane as shown.

point H

point X

point A

Line

A line has no thickness and has infinite length. It goes infinitely in both directions. It is represented by a straight edge having arrowheads on both ends. It is named with two capital letters with a small line and arrows at both ends (e.g.  $\overleftarrow{H}\overrightarrow{K}$ ). It can also be namedby a single italic lowercase letter (e.g. line g).

Plane

A plane is a flat surface extending indefinitely in all directions and it has no thickness, but with two dimensions, the length and width. A plane is commonly represented as a figure that can be named by a single letter or by three points not all in the same line. It can be named using a script capital letters or three capital letters (e.g. Plane AHX or Plane ℘).

Defined terms

Defined terms are terms with an exact definition or a specific description. They include a specific category and critical attributes. These terms are used to specify or describe different parts that will be used for theorems and other defined terms that we will encounter further in Geometry.

Examples of defined terms:

• Space - set of all points, boundless and three dimensional

• Collinear points - set of points that lie on the same line

• Noncollinear points - set of points that do not lie on the same line

• Coplanar points - set of points that lie on the same plane

• Noncoplanar points - set of points that do not lie on the same plane

Ray

Ray – a part of a line beginning at an endpoint and infinitely extended in one direction. To name a ray we usually start to an endpoint.

Line Segment

Line Segment - part of a line consisting of two points, called endpoints, and the set of all points between the two end points

Opposite Rays

Opposite Rays – are two rays that share the same endpoint but extends towards opposite directions

Angle

Angle – union of two noncollinear rays that share the same endpoint called the vertex. The two rays are referred to as the sides of the angle and the opening between the two rays determines the angle measure.

Activity

Choose the correct answer

Multiple Choice

Which of the following terms is not undefined?

• point

• angle

• plane

• line

Multiple Choice

How many points determine a line?

• 0

• 1

• 2

• 3

Multiple Choice

Which figure illustrates segment $\overline{AB}$ ?

Multiple Choice

Which of the following statements best describes a plane?

• It is a specific location in space

• It is a set of points the extends infinitely in either direction

• It is part of a line with two endpoints

• It is a set of points that forms a flat surface and it extends infinitely in all direction

Multiple Choice

A ray has _____ endpoint.

• 0

• 1

• 2

• 3