Why do chairs sometimes wobble?

1. Why do chairs sometimes wobble? • Have you ever noticed that a four legged chair sometimes wobbles, but a three- legged stool never wobbles?

2. Points, Lines and Planes Section 1.1

3. Points • An undefined term in geometry. (explained using examples and descriptions.) • They have no size • How do you represent a point? By using a dot • How do you label a Point? With a capital letter • Never use the same letter on two different points. • A point has neither shape nor size. • What are some examples of points? Stars, Corner of the room B A B X C

4. Lines • Undefined term in geometry. • They are made up of points and have no thickness or width. • There is exactly one line through two points • They Extend indefinitely • There are 2 Ways to label lines: 1. Using small script letter example: line t 2. Using any two points on the line – • Never name using three letters - t X Y Z X

5. Examples of lines: Phone lines strung between poles, spider webs, sun beams. Collinear Points: Points that lie on the same line. Non-collinear Points: Points that do not fall on the same line. A B A B

6. Planes • Undefined term in geometry • Are thought of as flat surfaces that extend indefinitely in all directions and have no thickness. • There are two ways to label planes: 1. Using a capital script letter – S 2. Using any three non-collinear points – XYZ, XZY, YXZ, YZX, ZXY, ZYX • Two planes intersect in one line. Y X Z S

7. Coplanar: Points that lie on the same plane. Non-coplanar: Points that do not lie on the same line.

8. Examples of planes • Top of desk • Wall • Chalkboard • Remember: A plane extends indefinitely in all directions. The examples above do not completely satisfy the description.

10. 102nd floor 82nd floor

11. Which tennis balls are coplanar?

12. Example: Use the figure to name each of the following. n Q 1. Give two other names for . • Give two other names for Plane R. • Name 3 collinear points. • Name 4 points that are coplanar. • Name a point that is not coplanar with points Q,S,and T. V m T P S R

13. Example: Draw and label a figure for each relationship. D B C P E A R

14. Space Is a boundless three dimensional set of all points. Space can contain lines and planes.

15. How many Planes are there? • Name three points that are collinear. • Are points A, B, C, & D coplanar? Explain. • At what point do and intersect?

16. How any planes are there? • Name three collinear points. • Are points G, A, B, & F coplanar? Explain • At what point do and intersect?

17. Points, Lines, and Planes As you look at the cube, the front face is on which plane? The back face is on which plane? The left face is on which plane? The back and left faces of the cube intersect at? Planes HGC and AED intersect vertically at? What is the intersection of plane HGC and plane AED?

18. Shade the plane that contains X, Y, and Z. Points X, Y, and Z are the vertices of one of the four triangular faces of the pyramid. To shade the plane, shade the interior of the triangle formed by X, Y, and Z. Points, Lines, and Planes

19. . Name each shaded plane 1-2

21. Activity • Each student gets two cards • Label one Q and one R. • Hold the two card together and place a slit halfway through both cards. • Hold cards so that the slits matchup and slide them together. (Tape cards together) • Where the cards meet models a line. Draw the line and label two points C and D on the line.

22. Activity Cont. • Draw point F on your model so that it lies in Q but not R. Can F lie on line DC? • Draw point G so that is lies in R but not Q. Can G lie on line DC? • If point H lies in both Q and R where would it lie? Draw it on your model. • Draw a sketch of your model on your paper. Label each thing appropriately.

23. HE Points, Lines, and Planes Use the diagram at right. 1. Name three collinear points. 2. Name two different planes that contain points C and G. 3. Name the intersection of plane AED and plane HEG. 4. How many planes contain the points A, F, and H? 5. Show that this conjecture is false by finding one counterexample: Two planes always intersect in exactly one line. D, J, and H planes BCGF and CGHD 1 Sample: Planes AEHD and BFGC never intersect.

24. Why do chairs sometimes wobble? • Have you ever noticed that a four legged chair sometimes wobbles, but a three legged stool never wobbles? This is an example of points and how they lie in a plane. Explain.