Geometry: Lesson 1.1 -- What is Geometry?
Geometry: Lesson 1.1 -- What is Geometry? Geometry Oklahoma Academic Standards:
G.RL.1.1 Understand the use of undefined terms, definitions, postulates, and theorems in logical arguments/proofs.
Lesson Objectives:
1. To understand the history of the subject. 2. To develop why we care about studying Geometry. 3. To develop how Geometry is structured.
Introduction: In this first lesson, we will discover the historical development of Geometry. In the process, we will also discover why we should care to learn about Geometry. Finally, we will learn how the subject is structured to process information.
To begin, let’s look at the word, Geometry, to find out what it actually means. Vocabulary: Definition – Geometry Geometry is made up of two affixes:
“Geo” which means ____________ and “Metry” which means _______________.
Therefore, Geometry is ______________________________________________________. The very core of the subject dates back to __________________ when the
Babylonian, Egyptian, Mayan, and Chinese Empires ruled their parts of the world. In those days, the importance of ________________________ for producing food is what led the
societies to develop many of the ideas used in the subject today. However, most of what the empires did wasn’t recorded.
It was only after a thousand years when ______________ of Miletus wrote what the
societies were doing in the first records of Geometry. After another few hundred years,
the mathematician ________________ put the pieces together to write the first textbook of Geometry: Lesson 1.1
1
Geometry, called “______________________”. This textbook written over 2,000 years ago is
essentially the same as the one we use today. This makes it the oldest known mathematics still studied today.
But why do we still study it? _____________________________, named after Euclid of
course, at it’s core is the foundation for countless subjects we take for granted everyday.
Practically, everywhere you look someone has used Geometry to do wonderful things. Examples of this include: _________________________________, __________________________________, and ______________________________ to name a few. It would be a safe bet to assume you will be using it in your future occupation. Remember though, Geometry at it’s core is about
measuring the Earth; so, you will probably be using many of the concepts learned in this class outside of the workplace, as well.
Assignment 1.1a You have the choice of the following:
1. Use the internet to look up 2 possible careers that you would like to do in the future. Write or
type a maximum of a 1-page report on those careers. To receive full credit, you must explain salary information in Oklahoma, skills required, education required, a basic overview of the job, and how Geometry is used in each career.
2. Use the internet to write a summary of one of the societies or mathematicians discussed in
today’s lesson. Describe when the society/person existed and what made them significantly important to us today. Be sure to list major discoveries or breakthroughs.
3. You may complete the Worksheet titled “Geometry: Handout 1.1a” and turn it in.
Geometry: Lesson 1.1
2
Now that we understand the historical development of the subject and why we should learn it, let’s understand how Euclid organized Geometry in his textbook. The subject of Geometry is structured using 4 concepts: ___________________ terms, ________________________, ____________________________, and ______________________.
To help us understand each of these concepts, we will use the game of Monopoly to describe each of these things.
Vocabulary: Definition – Undefined Term An undefined term is a word or phrase that has no definition. In other words, you can describe the word or phrase, but you can’t actually say what it is.
Examples: In the game of Monopoly, the ____________________ and _________________ are undefined terms.
Vocabulary: Definition – Definition An definition (or defined term) is a word or phrase that you can say what it is exactly.
Examples: In the game of Monopoly, the ____________________ and _________________ are definitions (defined terms). These are words typically found at the start or end of a rulebook.
Geometry: Lesson 1.1
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Vocabulary: Definition – Postulate A postulate is a phrase or sentence known to be true without question. These are sometimes known as unquestioned rules developed from undefined and defined terms.
Examples: In the game of Monopoly, _________________________________________________ and _____________________________________________________ are postulates. These are sentences typically found in the rulebook.
Vocabulary: Definition – Theorem A theorem is a phrase or sentence shown true with the use of arguments and reason. These are sometimes known as “house rules” developed from the other structures.
Examples: In the game of Monopoly, _________________________________________________ and _____________________________________________________ are theorems. These are sentences not typically found in the rulebook.
Through out the course, we will be looking at several of each kind of structure. Typically, the order in which we build a concept will be: first, agreeing upon undefined terms; second,
developing good definitions; third, developing a mutual understanding of postulates; and fourth, developing and reasoning new truths in the form of theorems.
Once we build the concept, we can begin to use the concept to solve problems both academically and with the goal of real-world use in jobs and life.
Geometry: Lesson 1.1
4
Assignment 1.1b You have the choice of the following:
1. Use your knowledge and the internet to choose 3 games. Write or type a description of
examples of undefined terms, definitions, postulates, and theorems for each game. Be sure to include a rough summary of the games.
2. Develop your own game. In the game, make sure you have clearly established the undefined
terms, definitions, postulates, and theorems. Be sure to include a rough summary of your game. Include a sample board or play through.
Geometry: Lesson 1.1
5
G.RL.1.1 Understand the use of undefined terms, definitions, postulates, and theorems in logical arguments/proofs.
Lesson Objectives:
1. To understand the history of the subject. 2. To develop why we care about studying Geometry. 3. To develop how Geometry is structured.
Introduction: In this first lesson, we will discover the historical development of Geometry. In the process, we will also discover why we should care to learn about Geometry. Finally, we will learn how the subject is structured to process information.
To begin, let’s look at the word, Geometry, to find out what it actually means. Vocabulary: Definition – Geometry Geometry is made up of two affixes:
“Geo” which means ____________ and “Metry” which means _______________.
Therefore, Geometry is ______________________________________________________. The very core of the subject dates back to __________________ when the
Babylonian, Egyptian, Mayan, and Chinese Empires ruled their parts of the world. In those days, the importance of ________________________ for producing food is what led the
societies to develop many of the ideas used in the subject today. However, most of what the empires did wasn’t recorded.
It was only after a thousand years when ______________ of Miletus wrote what the
societies were doing in the first records of Geometry. After another few hundred years,
the mathematician ________________ put the pieces together to write the first textbook of Geometry: Lesson 1.1
1
Geometry, called “______________________”. This textbook written over 2,000 years ago is
essentially the same as the one we use today. This makes it the oldest known mathematics still studied today.
But why do we still study it? _____________________________, named after Euclid of
course, at it’s core is the foundation for countless subjects we take for granted everyday.
Practically, everywhere you look someone has used Geometry to do wonderful things. Examples of this include: _________________________________, __________________________________, and ______________________________ to name a few. It would be a safe bet to assume you will be using it in your future occupation. Remember though, Geometry at it’s core is about
measuring the Earth; so, you will probably be using many of the concepts learned in this class outside of the workplace, as well.
Assignment 1.1a You have the choice of the following:
1. Use the internet to look up 2 possible careers that you would like to do in the future. Write or
type a maximum of a 1-page report on those careers. To receive full credit, you must explain salary information in Oklahoma, skills required, education required, a basic overview of the job, and how Geometry is used in each career.
2. Use the internet to write a summary of one of the societies or mathematicians discussed in
today’s lesson. Describe when the society/person existed and what made them significantly important to us today. Be sure to list major discoveries or breakthroughs.
3. You may complete the Worksheet titled “Geometry: Handout 1.1a” and turn it in.
Geometry: Lesson 1.1
2
Now that we understand the historical development of the subject and why we should learn it, let’s understand how Euclid organized Geometry in his textbook. The subject of Geometry is structured using 4 concepts: ___________________ terms, ________________________, ____________________________, and ______________________.
To help us understand each of these concepts, we will use the game of Monopoly to describe each of these things.
Vocabulary: Definition – Undefined Term An undefined term is a word or phrase that has no definition. In other words, you can describe the word or phrase, but you can’t actually say what it is.
Examples: In the game of Monopoly, the ____________________ and _________________ are undefined terms.
Vocabulary: Definition – Definition An definition (or defined term) is a word or phrase that you can say what it is exactly.
Examples: In the game of Monopoly, the ____________________ and _________________ are definitions (defined terms). These are words typically found at the start or end of a rulebook.
Geometry: Lesson 1.1
3
Vocabulary: Definition – Postulate A postulate is a phrase or sentence known to be true without question. These are sometimes known as unquestioned rules developed from undefined and defined terms.
Examples: In the game of Monopoly, _________________________________________________ and _____________________________________________________ are postulates. These are sentences typically found in the rulebook.
Vocabulary: Definition – Theorem A theorem is a phrase or sentence shown true with the use of arguments and reason. These are sometimes known as “house rules” developed from the other structures.
Examples: In the game of Monopoly, _________________________________________________ and _____________________________________________________ are theorems. These are sentences not typically found in the rulebook.
Through out the course, we will be looking at several of each kind of structure. Typically, the order in which we build a concept will be: first, agreeing upon undefined terms; second,
developing good definitions; third, developing a mutual understanding of postulates; and fourth, developing and reasoning new truths in the form of theorems.
Once we build the concept, we can begin to use the concept to solve problems both academically and with the goal of real-world use in jobs and life.
Geometry: Lesson 1.1
4
Assignment 1.1b You have the choice of the following:
1. Use your knowledge and the internet to choose 3 games. Write or type a description of
examples of undefined terms, definitions, postulates, and theorems for each game. Be sure to include a rough summary of the games.
2. Develop your own game. In the game, make sure you have clearly established the undefined
terms, definitions, postulates, and theorems. Be sure to include a rough summary of your game. Include a sample board or play through.
Geometry: Lesson 1.1
5
