MATHEMATICAL SYSTEM (UNDEFINED AND DEFINED TERMS)

MATHEMATICAL SYSTEM

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Undefined and Defined Terms

Beverly B. Cervantes

Math Teacher

Let us have a short review first.

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Choose the letter of the correct answer.

Multiple Choice

1. Which system or structure consists of both defined and undefined terms, axioms or postulates, and theorems?

• mathematical system

• organized system

• scientific system

• systematical system

Multiple Choice

2. What component of a mathematical system consists of a point, a line, and a plane?

• defined terms

• postulates

• theorems

• undefined terms

Multiple Choice

3. What component of a mathematical system includes a category or has definition such as a ray and an angle?

• defined terms

• postulates

• theorems

• undefined terms

Multiple Choice

4. Based on research of UP Diliman Institute of Biology, mangroves are better than dolomite for Manila Bay rehabilitation. What mathematical system is used in the given situation?

• defined terms

• postulates

• theorems

• undefined terms

Multiple Choice

5. What property of equality states that any number is equal to itself?

• Distributive

• Reflexive

• Symmetric

• Transitive

Let's get started!

Discussion Lesson

A mathematical system is a structure that consists of defined and undefined terms, axioms or postulates, and theorems. ​

There are four components of a mathematical system.

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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.

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There are three undefined terms:

1. Point

2. ​Line

3. Plane​

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Undefined Terms

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.

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point H

point X

point A

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1. Point

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. It can also be named by a single italic lowercase letter (e.g. line g).

2. Line

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 ℘).

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3. Plane

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.

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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

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Defined Terms

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​A, B, C, and D are non coplanar points.

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Examples of defined terms:

1. 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.

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Defined Terms

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

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Defined Terms

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

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Defined Terms

4. 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.​

Defined Terms

Multiple choice.

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Choose the letter of the correct answer.​

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Activity Time!

Multiple Choice

1. An angle whose measure is 90°.

• Obtuse angle

• Right angle

• Acute angle

• Ray

Multiple Choice

2. Points that lie on the same line.

• Collinear points

• Coplanar Points

• Non-collinear Points

• Non-coplanar points

Multiple Choice

3. A subset of a line with only one endpoint.

• Angle

• Line segment

• Ray

• Opposite rays

Multiple Choice

4. What is the common endpoint of the two rays in an angle?

• Angle measure

• Midpoint

• Arrowhead

• Vertex

Multiple Choice

5. A portion of a line with two end points.

• Angle

• Line segment

• Ray

• Opposite rays

Multiple Choice

6. A ray has _____ endpoint.

• 0

• 1

• 2

• 3

Multiple Choice

7. Which of the following statements best describes a plane?

• It is a specific location in space

• It is part of a line with two endpoints

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

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

Multiple Choice

8. How many points determine a line?

• 0

• 2

• 3

• 4

Multiple Choice

9. At least how many points determine a plane?

• 0

• 2

• 3

• 4

Multiple Choice

10. Which of the following statements is true?

• A point has thickness.

• A line segment continues indefinitely on only one side.

• A line segment continues indefinitely on only one side.

• A ray has only one endpoint.