The document discusses the mathematical system in geometry. It defines key undefined terms like point, line, and plane. It explains that a geometry system needs defined terms, undefined terms, postulates, and theorems. It then covers lessons about identifying points, lines, and planes; collinear and coplanar points/lines; and postulates related to points, lines, and planes. Specifically, it outlines four postulates: 1) through any two points there is exactly one line, 2) if two lines intersect they do so at exactly one point, 3) if two planes intersect they do so at exactly one line, and 4) through any three noncollinear points there is exactly one plane.

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.