Basic Undefined Terms in Geometry

BASIC UNDEFINED TERMS IN GEOMETRY

(Point, Line, and Plane)

OBJECTIVES:Describe the ideas of point, line, and plane

Identify real-life representations of point, line, and plane

Differentiate collinear points and noncollinear points

Distinguish coplanar lines from non-coplanar lines

What do they like?

Have you ever watched the stars at night?

Stars during the night look like DOTS.

A DOT suggests the idea of one of the basic undefined terms in Geometry which is the POINT.

Remember:We cannot define a point. We can just

describe it.

NAMEGRAPHICAL

REPRESENTATION

SYMBOL

DESCRIPTION

point A, point G, andpoint M

G

M A

A

G

M

A point has no length, width, or height.It indicates a position.

Table 1

Consider points G and M. If we will connect this two points, it will

introduce us another basic undefined term - the LINE. G M

GM read as line GM or MG read as line MG

NAMEGRAPHICAL

REPRESENTATION

SYMBOLDESCRIPTIO

N

line CD

and

line XY

C D m Y X n

CD, DC, or line m

XY, YX, or line n

A line has no width nor thickness but it has infinite length

Table 2

A B C D

Points A and B are collinear points.

Points C and D are also collinear points.

Why are they called collinear points?

_____________________________________________________________________________________________

F E H G Points E and G are noncollinear

points. Points E and H, points F and G,

and points F and H are also noncollinear.

Why are they called noncollinear points?

______________________________________________________________________________________________________

A B C D

Points A and B are collinear points.

Points C and D are also collinear points.

Why are they called collinear points?

They are called collinear point because they lie on the same line.

F E H G Points E and G are

noncollinear points. Points E and H, points F and

G, and points F and H are also noncollinear.

Why are they called noncollinear points?

They are called noncollinear because they DO NOT lie on the same line.

A set of three noncollinear points determines the third basic undefined term in geometry.

Consider the figure.

Noncollinear points P, Q, and R enclosed by a four-sided figure gives us plane PQR.

What is a plane?

PRQ

NAMEGRAPHICAL

REPRESENTATION

SYMBOL DESCRIPTION

Plane Q, Plane ABC,Plane BCA, or Plane CAB

A B C Q

ABC,

BCA,

CAB,

or Q

A plane has an infinite width and length but has no thickness.

Table 3

Coplanar and Non-coplanar Lines

Lines that lie on the same plane are called coplanar lines. Lines that do not lie on the same plane are called non-coplanar lines. Similarly:Points that lie on the same plane are called coplanar points.Points that do not lie on the same plane are called non-coplanar points.

AB

F E

D

C

HG

I

Activity 1:

In a group of five, identify representations of points, lines, and planes that you can see around the campus.

List as many as you can on your activity sheet.

Group Number:

Members:

Date:

Activity 1: REAL-LIFE REPRESENTATIONS OF UNDEFINED TERMS IN GEOMETRY

List real-life representations of points on the first column, of lines on the second column, and of planes on the third column.

POINTS LINES PLANES

Activity 2:

Identify the undefined term represented by each of the following physical examples.

1. Edge of a box kite

line

2. Brick wall

plane

3. Tip of a pen

point

4. Edge of a table

line

5. Face of a frame

plane

5. Poles

line

6. Cover of a book

plane

7. Needle point

point

8. Curtain rod

line

9. Crease of a paper

line

10. Tip of a leaf

point

Activity 3:Identify whether the given

points are collinear (CL), noncollinear (NC), coplanar (CP), or non-coplanar (NP). Put a check (/)under the proper column.

CL NC CP NP __ __ __ __ 1. Points G and P__ __ __ __ 2. Points F and J__ __ __ __ 3. Points F and I__ __ __ __ 4. Points C and E

E

H

G J P

C I

F

Activity 3: (continuation)

E

H

G J P

C I

F

CL NC CP NP

__ __ __ __ 5. Points G and H__ __ __ __ 6. Points E and D__ __ __ __ 7. Points J and J__ __ __ __ 8. Points H and F__ __ __ __ 9. Points I and J__ __ __ __ 10. Points C and I

Topic: BASIC UNDEFINED TERMS IN GEOMETRYReferences: 1. Geometry by E. Mapile 2. Geometry in the real world by K. D. Romero3. Geometry by A. A. Sarmiento & R. L. Villar 4. Geometry(a work text in Math III) by V. C. Tafalla, et

al.5. Secondary Mathematics Learning Competencies

(Mathematics III) A. 1.1 – 1.5

Prepared by: MS. DIVINA JOY A. VENTURAMA 202 (Instructional Materials Development with Computer

Literacy)

Summer; School Year 2009 - 2010