Chapter 1-2 Points, Lines, and Planes

2. Chapter 1-2Points, Lines, and Planes

3. Points, Lines, & Planes To understand basic terms and postulates of geometry. Objective

4. What is a definition? • Known words used to describe a new word Undefined terms – not formally defined There are 3 in geometry. Point Line Plane Segments, rays, and angles are defined in terms of these basic figures.

5. Example what your Cornell notes should look like now Points, Lines, & Planes Heading Objectives: Date: What is a definition Undefined terms……..

6. Point 1. Has no dimension (no length, width, thickness) 2. Usually represented by a dot 3. Named using one capital letter • B

7. Points • Points do not have actual size. • How to Sketch: Using dots • How to label: Use capital letters Never name two points with the same letter (in the same sketch). A B A C

8. Line • Extends forever in one dimension (length) • Has an arrowhead on each end representing the fact that it goes on forever • Consists of an infinite amount of points • Always straight l B A

9. Lines • Lines extend indefinitely and have no thickness or width. • How to sketch : using arrows at both ends. • How to name: 2 ways (1) small script letter – line n (2) any two points on the line - • Never name a line using three points - n A B C Lesson 1-1 Point, Line, Plane

10. Plane • Extends forever in 2 dimensions (length & width) • A flat surface consisting of infinitely many points • Usually represented by a 4-sided figure NOT THIS! THIS A W C B

11. Planes • How to sketch: Use a parallelogram (four sided figure) • How to name: 2 ways (1) Capital script letter – Plane M (2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C Horizontal Plane Vertical Plane Other

12. Different planes in a figure: A B Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc. D C E F H G

13. More Definitions • Collinear points – points that lie on the same line • Coplanar points – points that lie on the same plane

14. Practice : Naming Points • Name a point that is collinear with the given points • B and E: • C and H: • D and G: • A and C: • H and E: • G and B:

15. Name a point that is coplanar with the given points • M, N, R: • M, N, O: • M, T, Q: • Q, T, R: • T, R, S: • Q, S, O:

16. Coplanar Objects Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. Are the following points coplanar? A, B, C ? Yes A, B, C, F ? No H, G, F, E ? Yes E, H, C, B ? Yes A, G, F ? Yes C, B, F, H ? No Lesson 1-1 Point, Line, Plane

17. Line Segment (or segment) • A section of a line that has 2 endpoints • Named by its endpoints. AB or BA A B

18. Ray • Piece of a line with only one endpoint (initial point) and continues forever in the other direction • Named by the endpoint and a second point named on the ray. (name MUST begin with the endpoint!) AB A B

19. NAMING A RAY

20. Opposite Rays • 2 rays that share a common initial point and face opposite directions. • QP and QS are opposite rays. P Q S

21. A. Name 4 points in the figure. B. Name the two lines in the figure. C. Name the plane in the figure. D. Name four segments in the figure. E. Name four rays in the figure.

22. Postulate or axiom– an accepted statement of fact. Postulate 1-3 • Postulate 1-2 • Lines k and l have point A in common, so point A is the intersection • Two planes intersect in a line

23. INTERSECTING PLANES Name the intersection of each pair of planes Plane ABC and CGF CB Plane DHA and EHF HE Plane ABF and FGH EF CG Plane CBF and DHC

24. CLASSWORK PRACTICE • Textbook: PAGE 16 #8-24

25. The End

26. Modeling Activity

27. Activity Questions 1. When the cards are NOT together: What is the intersection of AB and CD? AB and EF? 2. With the cards together, what is the intersection of CD and EF? 3. What is the intersection of planes M and N? 4. Are CD and EF coplanar? Explain.