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MATHEMATICS 8
A MATHEMATICAL SYSTEM (UNDEFINED TERMS)
A mathematical system is a set of structures formed from one or more sets of undefined objects, various
concepts which may or may be not be defined, and a set of axioms relating these objects and concepts. It also
provides order and procedural operation in a certain discipline.
An axiomatic structure or axiomatic system is a collection of axioms, or statements about undefined
terms. You can build proofs and theorems from axioms. Logical arguments are built from with axioms.
Axioms are mathematical statements that serve as an entry statement in deriving other logically derived
statements. When proving a statement, a starting point must be first established and at the same time, assume
some statements are true.
Generally, there are two elements that compose a mathematical systemvocabulary and principles.
Vocabulary refers to either undefined terms or definition.
UNDEFINED TERMS
Undefined terms are terms that have not been previously categorically determined. These terms are
required to establish the definition of other terms. Geometry, as a mathematical system, is founded by the following
undefined terms:
POINTS - can be viewed as something
having specific position but without
dimension, magnitude or direction.
A dot usually represents a point and is
denoted by Capital Letter.
G
read as point G.
Examples:
1. Tip of a pen.
2. Corner of a paper.
LINES - Is a onedimensional figure
compose of infinite number of points. It
has unspecified length but without
width nor thickness.
The line below is line GN, written in
symbol 
󰇍
󰇍
󰇍
󰇍
󰇍
.
Examples:
1. A straight guitar string
2. Edge of a paper
PLANES -a plane is usually
represented by flat surface where
infinite number of lines can lie. It has a
specified width and length, but without
thickness
The plane below is “plane MAR” or plane
Y.
Examples:
1. Screen of a phone
2. A sheet of paper
ACTIVITY!
A. Identify if the given in the word pool is a POINT, LINE or PLANE.
A. the corner of the box B. tip of strand of hair C. surface of a table D. top of a box
E. side of a box F. Tip of rice grain G. straight wire H. the horizon
I. intersection of a ceiling and a wall J. Flooring
B. Name the points, lines and planes in the given figure below.
TRIANGLE CONGRUENCE
M
A
Y
R
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