What is geometry?
Blah, blah, blah...
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Postulates of Geometry
It would be impossible to even begin a study of geometry unless we accepted some basic rules called postulates.
Geometry's postulates deal with sets of points and their relationships, beginning with three "undefined" terms you have undoubtedly dealt with before: point, line and plane.
Our first postulate states the following:
Postulate 1
For any two points, there is exactly one line that contains them.
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Extending Vocabulary
Points that lie on the same line are called collinear points.
Lines that contain the same point are called concurrent lines.
Postulate 2
A line contains at least two points.
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Conditional statements
AStatements consisting of two clauses, one of which begins with the word "if" or "when" or some equivalent word are called conditional statements.
A conditional statement can be represented symbolically by "If a, then b, or even more briefly by
a b
The letter a represents the "if" clause, or hypothesis, and the letter b represents the "then" clause, or conclusion. The word
.
.
a
b
c
d
Extending Vocabulary
Now let's consider relationships between planes and points.
When we ust the term plane, we mean a flat surface that has no boundaries.
To represent a plane, draw and lable a rectangle. But, remember that even though your drawings will have boundareis, planes do not.
Postulate 3
For any three noncolinear points, there is exactly one plane that contains them..
