INTRODUCTION : The Basic Concept and Terms in Geometry

Introduction

       Etymology: Greek words Geo- "earth", -metri "measurement"  -- "Earth-measuring"

       Geometry is useful. As one might guess, geometry is used in advanced mathematics, such as it being applied in engineering and many skill trades. Geometry also enables one to learn what it means to prove a statement; generally, one will learn the ways of judging whether a bit of reasoning is true or not. More importantly, geometry provides a way of understanding the nature of mathematics as it is a logically organized subject.

       Finally, the study of geometry is fun. There is a thrill in learning new knowledge.

       In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line and plane, and are referred to as the "three undefined terms of geometry".

Task

Learning Objectives

After this lesson, the student will be able to:

  • define and list the characteristics of a point
  • describe a line and explain how it is geometrically written
  • discuss the geometric shape of a plane
Process

               - How does the author define a line?

               - How are lines labeled?

               - What are planes?

  • Afterwards, the student answer a short quiz.
      I. Multiple Choice
  1. Which of the following is not an undefined term in geometry?

          a. Point                   b. Line                c. Plane               d. Set/space     e. Quadrilateral

  1. Which of the following is the correct way of writing a point?

          a. P                         b. {P}                  c. plane P           d. line P             e. (P)

  1. Which shape is used to draw a plane on paper in geometry?

          a. Triangles            b. Quadrilaterals c.Lines               d.Circles            e. Points

 

      II. Essay

          In not more than 5 sentences, briefly discuss the relationships among the points, lines and planes.

Evaluation

                 ACTIVITY

           SCORES
VIDEOCLIP ACTIVITY                   10
TEST I.                    6
TEST II.                    5

                                           Total - 21pts

Notes:

     2pts are given to each correct answer in the videoclip activity.

     2pts for each item in Test I.

     20pts is the standard perfect score with 1pt as a bonus additional score to those who answered all questions satisfactorily.

Conclusion

       The 3 "undefined terms in geometry" are the building blocks for the rest of the subject. They are like big cinder blocks that are placed first at the bottom of the house -- without those blocks, the rest of the house can never be built.

       While these words are "undefined" in the formal sense, we can still "describe" these words. 
       The descriptions, stated below, refer to these words in relation to geometry.

 

POINT 
• a point indicates a location (or position) in space.
• a point has no dimension (actual size).  
• a point has no length, no width, and no height (thickness).
• a point is usually named with a capital letter.
• in the coordinate plane, a point is named by an ordered pair, (x,y).

While we represent a point with a dot, the dot can be very tiny or very large. Remember, a point has no size. 
points

The size of the dot drawn to represent a point makes no difference. Points have no size. They simply represent a location.

LINE (straight line)
• a line has no thickness.  
• a line's length extends in one dimension.
• a line goes on forever in both directions.
• a line has infinite length, zero width, and zero height. 
• a line is assumed to be straight.
• a line is drawn with arrowheads on both ends.
• a line is named by a single lowercase script letter, or by any two (or more) points which lie on the line. 
lines
Lines can be labeled with a single script letter, or by two points on the line, lineabnot. The thickness of a line makes no difference.
PLANE 
• a plane has two dimensions.
• a plane forms a flat surface extending indefinitely in all directions.
• a plane has infinite length, infinite width and zero height (thickness).
• a plane is drawn as a four-sided figure resembling a tabletop or a parallelogram.
• a plane is named by a single letter (plane m) or by three coplanar, but non-collinear,* points (plane ABC). 
plane

Plane m or Plane ABC.
While the diagram of a plane has edges, you must remember that the plane actually has no boundaries.

SPACE/SET

• basic structure in incidence geometry.

• consists of a set of elements called points, and a set of elements called lines.

• each line is a distinct subset of the points.

• the points in a line are said to be incident with the line.

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

Credits

https://study.com/academy/practice/quiz-worksheet-undefined-terms-of-geometry.html

https://study.com/academy/lesson/undefined-terms-of-geometry.html#lesson

https://study.com/academy/lesson/undefined-terms-of-geometry-lesson-plan.html

BUASEN, J.A Plane Geometry. Mathematics-Physics-Statistics Department, College of Arts and                Sciences, Benguet State University, La Trinidad, Benguet.