Geometry The word geometry comes from two Greek

Geometry The word "geometry " comes from two Greek words geo and metron meaning "earth measuring. " Geometry was extremely important to ancient societies and was used for surveying, astronomy, navigation, and building. Geometry, as we know it is actually known as Euclidean geometry which was written well over 2000 years ago in Ancient Greece by Euclid, Pythagoras, Thales, Plato and Aristotle just to mention a few. The most fascinating and accurate geometry text was written by Euclid, and was called Elements. Euclid's text has been used for over 2000 years!

Millenium Park Frank Lloyd Wright Millau Bridge Sir Norman Foster Fallingwaters Frank Lloyd Wright Point, Lines, Planes, Angles Components of Geometry Part 1

Components of Mathematical System Words and Statements 1. Undefined terms. 2. Definitions 3. Postulates 4. Theorems

Undefined Terms In geometry, definitions are formed using known words or terms to describe a new word. There are three words in geometry that are not formally defined. These three undefined terms are point, line and plane. PLP: Point, Line and Plane

Point Description A point has dimensions zero, a line is one-dimensional, a plane two-dimensional, and space is three-dimensional. What might be a four-dimensional concept?

Point POINT (an undefined term) In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, (x, y). Do you get the point?

Lines Description A line is a series of consecutive points going in opposite directions. It is of infinite length. Like a point it has no thickness. It is represented as a line with arrows on each end to indicate the line keeps going.

Planes Description A plane is a flat surface that extends outward in all directions. It can be thought of as a set of consecutive lines extending in opposite directions.

Planes A A plane is usually indicated by a parallelogram. Although edges are drawn, they are not really there. The figure is only a model of the plane. The plane extends outward infinitely. The letter in the corner is the name of the plane: plane A.

Why Undefined terms? Circular Definitions How do you define the first word without other words? Have you ever looked up a word that was explained in terms of another word that you did not know? Have you looked up the new word to find that it was defined in terms or the first word? This can be a real problem. In foreign languages this happens all the time. This also happens in geometry.

Geometric Example Definition #1 A point is the intersection of two lines. Definition #2 A line is a continuous series of points going in opposite directions.

What is wrong? 1 You need to know what a line is to define a point. 2 You need to know what a point is to define a line. This is a never ending cycle.

Revisited Definition #1 A point is the intersection of two lines. Definition #2 A line is a continuous series of points going in opposite directions.

Definition #1 A point is the intersection of two lines. Definition #2 A line is a continuous series of points going in opposite directions. But you say that you can see it. What if you were blind?

Definitions There a lot of terms in geometry – 7 pages of them. There are too many definitions to memorize. Therefore, you need to understand how to write definitions. If you have this skill, your understanding will enable you to define any term without having to memorize.

A description is not a definition. A definition gives the minimal characteristics that include all possible variations or elements.

To define terms there is a 5 step process: 1 Categorize 2 Characterize 3 Clear 4 concise 5 Reversible

We will start with non-geometric terms. To define terms there is a 5 step process: 1 Categorize: put the term in 2 Characterize 3 Clear 4 concise 5 Reversible

We will start with non-geometric terms. 1 Categorize: put the term into a category that restricts what you are talking about. A canoe is… a boat

We will start with non-geometric terms. 2 Characterize: list the minimum characteristics to A canoe is… a boat long thin open propelled by paddles.

3 Clear: easily understood, non-complex. 4 concise: short as possible. 5 Reversible: if read backward then the definition still works. A canoe is… a long thin open boat Yes to all three. propelled by paddles. 3 It is easily understood. 4 No words can be left out. 5 When read backwards it is complete and works.

Again we will start with non-geometric terms. 1 Categorize: put the term into a category that restricts what you are talking about. A watch is… a time piece

2 Characterize: list the minimum characteristics to A watch is… a time piece that one wears on your wrist.

3 Clear: easily understood, non-complex. Yes 4 concise: short as possible. Yes 5 Reversible: if read backward then the definition still works. No! A watch is… a time piece that one wears on your wrist.

3 Clear: easily understood, non-complex. Yes 4 concise: short as possible. Yes 5 Reversible: if read backward then the definition still works. A watch is… a time piece that one wears Now, on your wrist. yes! Or in your pocket.

Note: that when read backwards it was noted that pocket watches were left out. Reversibility is the test for a complete definition.

Note: that all definitions start the same way. A _____ is … A house is … A circle is … A parallelogram is …

Let’s Practice Step 1 We will practice step 1 - Categorize A woman is … a female A car is … A sandal is … A lake is … a vehicle a shoe a body of water A pencil is … a writing instrument

Let’s Practice Step 1 We will practice step 1 - Categorize A girl is … A bus is … a female a vehicle A vase is … a container A pot is … a container A strait is … a poker hand

Let’s Practice Step 2 We will practice step 2 - Characterize A woman is … a female older than 17 a vehicle with 3 or 4 wheels A car is … for 6 or less people. motorized A sandal is … a shoe with top open to the air. open A lake is … a body of water large surrounded by land. A pencil is … a writing instrument that leaves a carbon mark.

Let’s Practice Step 2 We will practice step 2 - Characterize A girl is … a female A bus is … a vehicle that transports motorized 12 or more people. A vase is … a container for flower open A pot is … less than 17. a container arrangements. with a lid used for cooking. A strait is … a poker hand with 3 of a kind and 2 of a kind.

C’est fini. Good day and good luck.