Post on 18-Apr-2015
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