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```When studying Geometry we use:
Undefined terms
When studying Geometry we use:
Undefined terms
Assumptions know as postulates or
axioms
When studying Geometry we use:
Undefined terms
Assumptions know as postulates or
axioms
Definitions
When studying Geometry we use:
Undefined terms
Assumptions know as postulates or
axioms
Definitions
Theorems and other conclusions
Two undefined terms:
point
line
Postulates or axioms are statements
assumed to be true without proof.
Postulates or axioms are statements
assumed to be true without proof.
An example of a postulate:
Any segment or angle is congruent to
itself. (Reflexive Property)
We have looked at two theorems so
far:
We have looked at two theorems so
far:
Theorem 1: If two angles are
right angles, then they are
congruent.
We have looked at two theorems so
far:
Theorem 1: If two angles are
right angles, then they are
congruent.
Theorem 2: If two angles are
straight angles, then they are
congruent.
Among the terms already defined in
this set of lessons are:
line segment, ray, angle, congruent,
acute angle, right angle, obtuse angle,
straight angle, polygon, triangle,
collinear, theorem, midpoint, trisection
points, angle bisector, angle trisectors,
and postulate.
Another definition
Definition: A definition states the
meaning of a term or idea.
Definitions can be written as
conditional statements.
Definitions can be written as
conditional statements.
Conditional statements are written in
the form:
If p, then q
where p and q are declarative
statements.
If p, then q
The "if" part (p) of a statement is
called the hypothesis, and the "then"
part (q) is called the conclusion.
Another way to write
"If p, then q" is
Right angle: A right angle is an
angle with a measure of 90º.
Right angle: A right angle is an
angle with a measure of 90º.
If an angle is a right angle, then it
has a measure of 90º.
Right angle: A right angle is an
angle with a measure of 90º.
If an angle is a right angle, then it
has a measure of 90º.
Converse:
If an angle has a measure of 90º,
then it is a right angle.
is the converse of
is the converse of
The converses of all definitions are
true statements.
The converses of theorems and
postulates are not always true.
Theorem 1: If two angles are right
angles, then they are congruent.
Converse is false:
If two angles are congruent, then
they are right angles.
When studying Geometry we use:
undefined terms, definitions,
postulates, and theorems.
When studying Geometry we use:
undefined terms, definitions,
postulates, and theorems.
Definitions can be written as
conditional statements
.
When studying Geometry we use:
undefined terms, definitions,
postulates, and theorems.
Definitions can be written as
conditional statements
.
The converses
of all
definitions are true.
When studying Geometry we use:
undefined terms, definitions,
postulates, and theorems.
Definitions can be written as
conditional statements
.
The converses
of all
definitions are true.
Not all converses of postulates and
theorems are true.
```
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