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Introduction to Geometry – Postulates and Theorems This first section introduces you to terms that we will be using throughout the course. I would not.

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Presentation on theme: "Introduction to Geometry – Postulates and Theorems This first section introduces you to terms that we will be using throughout the course. I would not."— Presentation transcript:

1 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.

2 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

3 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.

4 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.

5 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.

6 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.

7 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

8 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… Introduction to Geometry – Postulates and Theorems StatementsReasons Definition of perpendicular Proven theorems, definitions, or postulates

9 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… Introduction to Geometry – Postulates and Theorems StatementsReasons 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

10 Lets set up a simple proof so you can see what it looks like. Given :AB is intersecting CD at E AB is perpendicular to CD Prove :angle AEB = angle CED Introduction to Geometry – Postulates and Theorems StatementsReasons A B C D E

11 Lets set up a simple proof so you can see what it looks like. Given :AB is intersecting CD at E AB is perpendicular to CD Prove :angle AEB = angle CED Introduction to Geometry – Postulates and Theorems StatementsReasons Angles AEC, CEB, BED, and AED are all right angles A B C D E

12 Lets set up a simple proof so you can see what it looks like. Given :AB is intersecting CD at E AB is perpendicular to CD Prove :angle AEB = angle CED Introduction to Geometry – Postulates and Theorems StatementsReasons Angles AEC, CEB, BED, and AED are all right angles Theorem – if two lines are perpendicular, they form four right angles A B C D E

13 Lets set up a simple proof so you can see what it looks like. Given :AB is intersecting CD at E AB is perpendicular to CD Prove :angle AEB = angle CED Introduction to Geometry – Postulates and Theorems StatementsReasons 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° A B C D E


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