Download Introduction to Geometry – Postulates and Theorems

Introduction to Geometry – Postulates and Theorems
This first section introduces you to terms that we will be using throughout the
course. I would not go about memorizing these but you must understand how
they are used. So I would write out the definition of a postulate or theorem,
and then describe in your own words how it is utilized.
Introduction to Geometry – Postulates and Theorems
This first section introduces you to terms that we will be using throughout the
course. I would not go about memorizing these but you must understand how
they are used. So I would write out the definition of a postulate or theorem,
and then describe in your own words how it is utilized.
Definitions – statements that distinguish one term from all other terms
Triangle – an enclosed three sided figure
Square – an enclosed four sided figure, all sides have equal measure and all
angles are right angles
Introduction to Geometry – Postulates and Theorems
This first section introduces you to terms that we will be using throughout the
course. I would not go about memorizing these but you must understand how
they are used. So I would write out the definition of a postulate or theorem,
and then describe in your own words how it is utilized.
Definitions – statements that distinguish one term from all other terms
Triangle – an enclosed three sided figure
Square – an enclosed four sided figure, all sides have equal measure and all
angles are right angles
Each definition names the term, defines which set it belongs to ( both are figures ),
and states the properties that distinguish it from other terms.
Introduction to Geometry – Postulates and Theorems
This first section introduces you to terms that we will be using throughout the
course. I would not go about memorizing these but you must understand how
they are used. So I would write out the definition of a postulate or theorem,
and then describe in your own words how it is utilized.
Definitions – statements that distinguish one term from all other terms
Triangle – an enclosed three sided figure
Square – an enclosed four sided figure, all sides have equal measure and all
angles are right angles
Each definition names the term, defines which set it belongs to ( both are figures ),
and states the properties that distinguish it from other terms.
Postulates – statements that are generally accepted as true
Every line contains at least two points.
Introduction to Geometry – Postulates and Theorems
This first section introduces you to terms that we will be using throughout the
course. I would not go about memorizing these but you must understand how
they are used. So I would write out the definition of a postulate or theorem,
and then describe in your own words how it is utilized.
Definitions – statements that distinguish one term from all other terms
Triangle – an enclosed three sided figure
Square – an enclosed four sided figure, all sides have equal measure and all
angles are right angles
Each definition names the term, defines which set it belongs to ( both are figures ),
and states the properties that distinguish it from other terms.
Postulates – statements that are generally accepted as true
Every line contains at least two points.
Postulates help us to state simple facts; in this case referring to lines. Postulates help
us draw valid conclusions about complex problems. Sometimes they describe
relationships between geometric figures.
Introduction to Geometry – Postulates and Theorems
This first section introduces you to terms that we will be using throughout the
course. I would not go about memorizing these but you must understand how
they are used. So I would write out the definition of a postulate or theorem,
and then describe in your own words how it is utilized.
Theorems – statements that must be proved before they are accepted as being true
Theorem - If two lines are perpendicular, they form four right angles.
To prove this theorem we need to know the definition of perpendicular.
Perpendicular Lines – lines that intersect each other at a 90° angle.
Introduction to Geometry – Postulates and Theorems
This first section introduces you to terms that we will be using throughout the
course. I would not go about memorizing these but you must understand how
they are used. So I would write out the definition of a postulate or theorem,
and then describe in your own words how it is utilized.
Theorems – statements that must be proved before they are accepted as being true
Theorem - If two lines are perpendicular, they form four right angles.
To prove this theorem we need to know the definition of perpendicular.
Perpendicular Lines – lines that intersect each other at a 90° angle.
To prove theorems you might need an illustration.
The illustration helps show how the lines are perpendicular
Introduction to Geometry – Postulates and Theorems
Proof – a formal process used to demonstrate the truth of a statement
To prove something in geometry you need to set up a series of logically
related statements that lead to some previous conclusion. They are set up as a
table…
Statements
a b
Reasons
Definition of perpendicular
Proven theorems, definitions, or postulates
Introduction to Geometry – Postulates and Theorems
Proof – a formal process used to demonstrate the truth of a statement
To prove something in geometry you need to set up a series of logically
related statements that lead to some previous conclusion. They are set up as a
table…
Statements
a b
Reasons
Definition of perpendicular
Proven theorems, definitions, or postulates
Direct Proof – shows that a statement is true because a logical chain of steps
supports it.
Indirect Proof – shows that a statement can not be false, therefore it must be true
Introduction to Geometry – Postulates and Theorems
Let’s set up a simple proof so you can see what it looks like.
C
Given : AB is intersecting CD at E
AB is perpendicular to CD
B
A
E
Prove : angle AEB = angle CED
D
Statements
Reasons
Introduction to Geometry – Postulates and Theorems
Let’s set up a simple proof so you can see what it looks like.
C
Given : AB is intersecting CD at E
AB is perpendicular to CD
B
A
E
Prove : angle AEB = angle CED
D
Statements
Angles AEC, CEB, BED, and AED
are all right angles
Reasons
Introduction to Geometry – Postulates and Theorems
Let’s set up a simple proof so you can see what it looks like.
C
Given : AB is intersecting CD at E
AB is perpendicular to CD
B
A
E
Prove : angle AEB = angle CED
D
Statements
Reasons
Angles AEC, CEB, BED, and AED
are all right angles
Theorem – if two lines are perpendicular, they form
four right angles
Introduction to Geometry – Postulates and Theorems
Let’s set up a simple proof so you can see what it looks like.
C
Given : AB is intersecting CD at E
AB is perpendicular to CD
B
A
E
Prove : angle AEB = angle CED
D
Statements
Reasons
Angles AEC, CEB, BED, and AED
are all right angles
Theorem – if two lines are perpendicular, they form
four right angles
Angle AEB = angle CED
Definition – the degree measure of a right angle is
90°