Mathematical system

1. Mathematical System in
Geometry
Mathematics 8 – Quarter 3: Module 1 (MELC Based)

2. Learning Competencies
Illustrates the need for an axiomatic structure of a
mathematical system in general, and in Geometry in
particular: (a) defined terms; (b) undefined terms;(c)
postulates; and (d) theorems (M8GE-IIIa-c-1).

3. Objectives
At the end of the lesson, you are expected to:
 identify and illustrate the points, lines and planes;
identify and illustrate collinear points and coplanar
points/lines and
determine the postulates that are related to points,
lines and planes.

4. LESSON 1: Undefined Terms
 In Geometry, we have several undefined terms: point, line and
plane.
UNDEFINED TERMS
TERM DESCRIPTION HOW TO NAME IT DIAGRAM
A point indicates a location and
no size.
You can represent a point by a dot
and name it by a capital letter, such
A.
A line is represented by a straight
path that extends in two opposite
directions without end and has no
thickness. A line contains infinitely
many points.
You can name a line by any two
points on the line, such as 𝐴𝐵 (read
“line AB”) or 𝐵𝐴, or by a single
lowercase letter, such as line 𝓁.
A plane is represented by a flat
surface that extends without end
and has no thickness. A plane
contains infinitely many lines.
You can name a plane by a capital
letter, such as plane P
, or by at least
three points in the plane that do not
all lie on the same line, such as plane
ABC.

5. LESSON 1: Exercise
Tell whether each of the following represents a point, a
line, or a plane.
Example: top of a box; plane
1. four corners of a room
2. cover of a book
3. side of a blackboard
4. tip of a pen

6. LESSON 2: Collinear and Coplanar

7. LESSON 2: Exercise
Use the figure on the right to name each of the
following:
Example: three collinear points: Points A,P
,B; Points
C,P
,D; Points J,D,K
1. three noncollinear points
2. four coplanar points
3. four noncoplanar points

8. LESSON 3: Postulates about Points, Lines
and Planes
POSTULATE 1
Through any two points there is exactly one line.
POSTULATE 2
If two distinct lines intersect, then they intersect in exactly
one point. 𝐴𝐸 and 𝐷𝐵 intersect in point C.
POSTULATE 3
If two distinct planes intersect, then they intersect in exactly
one line.
Plane W and plane R intersect in line 𝓁 .
POSTULATE 4
Through any three noncollinear points there is exactly one
plane. Points A, B, and C are noncollinear. Plane P is the
only plane that contains them.

9. LESSON 3: Exercise
Determine what postulate is to be used to justify each of the
following statements.