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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,
adjacent angles, union, intersection,
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.