Geometry What is it?

The word "geometry" geo + metry means "earth + to measure." Geometry was probably first developed to measure the earth and its objects. The word "geometry" geo + metry means "earth + to measure." Surveying land, designing buildings, and measuring commodities were probably important early on in people's history.

A knowledge of basic geometry is useful in everyday life. It is useful for measuring and designing. For example, carpeting a room, painting a house, building a picture frame, etc.

History Egyptians 2000 –500 B.C. Practical knowledge through surveying and constructions Babylonians 2000-500 B.C. Pythagorean relationships Greeks 750-250 B.C. First formal mathematics “rules of logic”

History Continued..... The Fifth Postulate Controversy 400 B.C.-1800A.D. The Search for Pi() ???-present Coordinate Geometry 1600 A.D. Non-Euclidean Geometries early 1800’s Differential Geometry late 1800’s –1900’s Fractal Geometry late 1800’s –1900’s

The leading mathematics teacher of all time. Euclid was a very common name around this period Euclid was the leader of a team of mathematicians working at Alexandria Euclid's most famous work is his treatise on mathematics The Elements. The book was a compilation of knowledge that became the centre of mathematical teaching for 2000 years.

Euclid Born Approx. 300BC Residence Alexandria, Egypt Nationality Greek Field Mathematics Known for Euclid’s Elements Justin van Ghent’s 15th-century depiction of Euclid.

Euclid taught at the University at Alexandria, the main seaport of Egypt, Since Euclid’s time, the Elements had been translated into more languages and published in more editions than any other book except the Bible. Although very little of the mathematics in the Elements was original, what made the book unique was its logical organization of the subject, beginning with a few simple principles and deriving from them everything else.

Let’s begin……

Vocabulary Live it Learn it KNOW IT!

Today you will learn: Points Lines Planes Intersections

Examples:

g How many different ways can you name this line? C B A What are A, B, C?

Use the figure to name each of the following: A line containing point N A plane containing points P and M

Plane ABCD intersects Plane BCFG where? Plane EADH intersects Line AB where? Plane DCEF intersects Plane ABEF? Line AB intersects Line BF where?

Name a fourth point that is in the same plane as the given points. A, D, B, ? E, H, G, ?

Are points R, W, S coplanar?

Points We may think of a point as a "dot" on a piece of paper. We identify this point with a letter. A point has no length or width, it just specifies an exact location. Example: The following is a diagram of points A, B, C, and Q:                         A point is one of the basic terms in geometry. Everything is based on points in geometry. C A Q B

Vocabulary Word - Define Picture Name Point- Name with a capital letter Point W A dot No length or width W

How many points are on

Space – all points

Lines A set of points In geometry, a line extends forever in both directions. We write the name of a line passing through two different points A and B as "line AB" or as AB. Also by a single lower case letter. Example: The following is a diagram of three lines: line AB,line HG and line j.                                                           j

Vocabulary Word - Define Picture Name Line- h B A set of many points Extends in both directions forever AB Or Line h A

How many points make up a line?

How many lines can you find through point B?

Collinear points All points are in one line. Noncollinear Points

Vocabulary Word - Define Picture Name Collinear- All points are in one line.

Planes A flat surface. A plane extends without ending. Has no thickness. N Plane M and Plane N M

Vocabulary Word - Define Picture Name Planes B Name with one capital letter Plane W Or Using all letters at vertices Plane ABCD A A flat surface. A plane extends without ending. W D C

Example: How many planes appear in this figure?

Vocabulary Word - Define Picture Name Coplanar All points all in one plane.

Intersection The term intersect is used when lines, rays, line segments or figures meet, that is, they share a common point. The point they share is called the point of intersection. We say that these figures intersect. Example: In the diagram below, line AB and line GH intersect at point D:                                      

Vocabulary Word - Define Picture Name Intersection The point they share is called the point of intersection.

Line j and k intersect where? Examples: T Line j and k intersect where? j Line j and k intersect at point T k TWO LINES WILL ALWAYS INTERSECT AT ONE POINT!

A PLANE AND A LINE WILL ALWAYS INTERSECT AT ONE POINT! Name a line correctly. Line CB intersects Plane M where?

What is the intersection of two planes? Name the two planes. What is the intersection of two planes? TWO PLANES WILL ALWAYS INTERSECT AT ONE LINE! Figure 3 Plane G and Plane H Plane G and Plane H intersect at line segment XY Line XY is in Plane G and Plane H G Y H X

Expected to know: Points Naming Points Lines Naming Lines Collinear Planes Naming Planes Coplanar Intersections Identify type of intersection Expected to know:

Remember to read carefully!!

Page 7 Class exercises # 1-20

Endpoints An endpoint is a point used to define a line segment or ray. A line segment has two endpoints; a ray has one. Example: The endpoints of line segment DC below are points D and C, and the endpoint of ray MN is point M below:                                                          

Vocabulary Word - Define Picture Name Endpoint- a point used to define a line segment or ray

Line Segments A line segment does not extend forever. It has two distinct endpoints. We write the name of a line segment with endpoints A and B as "line segment AB" or as AB. Example: The following is a diagram of two line segments: line segment CD and line segment PN.                                                              

Vocabulary Word - Define Picture Name Line Segment- does not extend forever has two distinct endpoints CD

Rays We may think of a ray as a "straight" line that begins at a certain point and extends forever in one direction. The point where the ray begins is known as its endpoint. We write the name of a ray with endpoint A and passing through a point B as "ray AB" or as AB. Example: The following is a diagram of two rays: ray HG and ray AB.                                                              Note how the arrow heads denotes the direction the ray extends in: there is no arrow head over the endpoint.

Vocabulary Word - Define Picture Name Ray- a "straight" line that begins at a certain point and extends forever in one direction B A AB