1. Bell Work Use the following “Geometry” words in regular English sentences. Underline or highlight the words in your sentences. point line plane angle ray space Example: Example: Get the point?Get the point NOTE NOTE: Your Bell Work sheet goes in your 3-ring binder. If you do not yet have a 3 ring binder write it on a piece of paper. If you have not finished setting up your glossary, please do it now. You will be excused from the Bell Ringer because we will be using the Glossary A LOT this period.

2. Points, Lines and Planes Objective To understand basic terms and postulates of geometry. Write this in your Table of Contents with your starting page number. In this case it should be 3. At the start of your daily notes you should write the Date, the Title and the Objective.

3. OH Standards  3108.1.4 Recognize that a definition depends on undefined terms and on previous definitions.  SPI 3108.1.3 Use geometric understanding and spatial visualization of geometric solids to solve problems and/or create drawings.  SPI 3108.1.4 Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems.  CLE 3108.4.1 Develop the structures of geometry, such as lines, angles, planes, and planar figures, and explore their properties and relationships.

4. Materials  Notebook  Straight Edge  Pencil Nature’s Great Book is written in mathematical symbols. ~ GALILEO GALILEI Nature’s Great Book is written in mathematical symbols. ~ GALILEO GALILEI

5. Math and other Foreign Languages WWhen you learn a new language, you learn the basic words first. GGeometry is the same. TThere will be LOTS of vocabulary in this first chapter. BBe sure to keep a good glossary so new words can be easily found.

6. Building Blocks of Geometry  Three building blocks of geometry are points, lines, and planes.  A point is the most basic building block of geometry.  You should already know this definition. Poi nt : It has no size. It has only location. You represent a point with a dot. You name it with a capital letter. The point shown is called P. P

7. Points  A tiny seed is a “real world” example of a point. A point, however, is smaller than any seed that ever existed.  Can you think of any other “real world” examples of points?

8.  Copy the description. Leave room for a diagram, as shown.  Next to the description, draw Points A and B.  Use a straightedge to draw a mark through both dots.  Draw arrows at the ends of the line.  Label it “m.” L Lin e : A line is a straight path. It has no thickness. It extends forever. The line shown is named AB, BA or m. Glossary: Line B A How many different ways can you place it so it touches both points? Is a ruler the only straight edge you could use? Why do we draw arrows? m When would we use this? Why can the name go in either direction? Notice that we use the arrow symbol above the name.

9. Representing Lines  A piece of spaghetti is a physical model of a line. A line, however, is longer, straighter, and thinner than any piece of spaghetti ever made.  Can you think of any other real world representations of lines?

10. Postulates and Points  Glossary:  Glossary: Postulate – an accepted statement of fact. Also called an axiom.  You demonstrated with your straightedge that you could only line it up against the points in exactly one way. We can’t prove it but we can demonstrate over and over.  Copy this postulate into the Postulates and Theorems section of your notebook. POSTULATE: Through any two points you can draw exactly one line.

11. Glossary: Planes  A plane is a flat surface that has no thickness and extends forever.  Name a plane using a script capital letter or three points not on a line.  Write the description and draw this diagram in your glossary  Usually planes are drawn as a parallelogram.  This plane is named R or ABC. A C B R Why can’t the points be on the same line?

12. Naming Planes  When you name a plane from a figure, with more than three points, list the corner points in consecutive order.  For example, plane ABCD and ADCB are names for the plane on the top of the box.  Plane ACBD is not. A C D B

13. Representing Planes  A flat piece of rolled out dough is a physical model of a plane. A plane, however, is broader, wider and flatter than any piece of dough could ever roll.  Can you think of any other real world representations of planes?

15.  Point, Line and Plane are considered to be undefined.  It can be difficult to explain what points, lines, and planes are even though you may recognize them.  Early mathematicians tried to define these terms.  Those definitions don’t help much, do they? Undefined Terms The ancient Greeks said, A point is that which has no part. A line is breadthless length. The Mohist philosophers of ancient China said, The line is divided into parts, and that part which has no remain- ing part is a point.

16. Undefined Terms  It is impossible to define point, line, and plane without using words or phrases that themselves need definition. So these terms remain undefined.  Yet, they are the basis for all of geometry.  Using the undefined terms point, line, and plane, you can define all other geometry terms and geometric figures.  I will give you many definitions, and others will be defined by you and your classmates.

17. Space, the Final Frontier  How would you define space?  Every object is made up of a set of points.  Glossary  Glossary: Space – the set of all points in three dimensions.

18. Glossary: Glossary: Collinear  Collinear points are points on the same line.  Now are the points collinear? Why or why not?  Is there any way to draw one line through all three points now?

19. Glossary: Glossary: Coplanar  Coplanar points are points in the same plane.  Are these points collinear?  Points A, B and C are coplanar in Plane R.  Are they coplanar in Plane S? R S A B C NO NO

20. Ball A is in the pocket. Ball C is on the racket. All other balls are on the court. Name three balls that are collinear Name three balls that are coplanar but not collinear. Name four balls that are not coplanar.

21. How many points make a plane  Photographers use three-legged tripods to make sure that a camera is steady.  The feet of the tripod all touch the floor at the same time.  You can think of the feet as points and floor as a plane.  As long as the feet do not all lie on one line, they lie in exactly one plane.  Postulate  Postulate: Through any three noncollinear points there is exactly one plane. X Y Z R What is noncollinear and why do the points have to be noncollinear?

22. Putting it all together. 1. What are two other ways to name DJ ? line l and JD. 2. Name three collinear points A, P, B; others 3. What are two other ways to name plane R? APD and CPB, others 4. Name four coplanar points APBC, others 5. Name four noncoplanar points Any three points and point J l m Why is this line dotted?

23. S Segme nt : A line segment is the part of the line consisting of two points and all the points between them. The segment is named AB or BA Glossary: Glossary: Segment A B Note that a segment symbol has no arrows.. How many points are between points A and B?.

24. Glossary: Glossary: Rays and Endpoints Ray : A ray is a part of a line. It starts at an endpoint. It extends forever in one direction. This ray is named by writing AB The endpoint is always written first when naming a ray. A B Point A is called the endpoint of ray AB. Why does the ray symbol have one arrow? R E Endp oint : a point at one end of a segment or a point at one end of a ray. A B A B

25. A Final word on Rays  Give real world situations that can be modeled by rays.  How are rays and segments the same? They are both parts of a line.  How are rays and segments different? Rays only have one endpoint.

26. Opposite Rays O  Draw a line on the right half of the O glossary page.  Mark point A in the middle of it.  Mark points B and C on either side of Point A  These are opposite rays.  Glossary  Glossary: Opposite Rays They share a common endpoint They point in opposite directions They form a straight line.  Write the names of two rays starting from point A. AB and AC A B C

27. Got it? - DRAW THE PICTURE!  Names of six segments in the figure.  Names six rays in the figure.  Name a set of opposite rays. E F D

28. Classwork / Homework Classwork  Think About a Plan Homework  Practice Part 1