Warm-up

1. Warm-up Show that the following conjecture is not true by finding a counterexample. Conjecture: All odd numbers can be expressed as the sum of two primes.

2. Directions: In a few sentences, describe as many of the words below. point line plane collinear coplanar segment endpoint initial point ray opposite ray

3. Chapter 1.2: Points, Lines, and Planes • Students will identify and apply basic definitions of geometry.

4. A point is an exact location in space. You are here.

5. A true point has no length, no width, and no height. In fact, you cannot see a true point.

6. A point is named by a letter. Point P P

7. Lines are 1-dimensional objects that have only length. Lines continue forever in both directions.

8. Because a line has no width or height, you cannot see a true line.

9. A line is defined by 2 points. A B line AB or line BA

10. Collinear Points Collinear points are points that lie on the same line. (The line does not have to be visible.) Collinear A B C C A Non collinear B

11. A ray has an initial point but no ending point. initial point

12. A ray of light has an initial point (like the sun) and continues forever in the same direction.

13. Of course, if the ray hits an object, the light could be absorbed or reflected. MIRROR

14. A ray is also defined by 2 points. C D Ray CD

15. If C is between A and D, then CD and CA are opposite rays A C D ray CD and ray CA

16. A line segment has a starting point and an ending point. Line segments can be measured.

17. A line segment also defined by 2 points. E Line Segment EF or FE F

18. Lines can do various things.

19. Lines can intersect at a point to form angles. X Y Z

20. Angles are defined by 3 points. X Y Z XYZ

21. These angles can be right angles. 90 

22. These angles can be right angles. R USR = 90⁰ RST = 90⁰ c S T U USV = 90⁰ TSV = 90⁰ V

23. When lines intersect to form right angles, they are said to be perpendicular. R UT RV c S T U V

24. Lines can intersect to form acute and obtuse angles. 45 acute 135 obtuse

25. Lines can also run into each other to form straight angles.

26. 180 is a straight angle

27. Lines do not always intersect.

28. Lines can be parallel.

29. Parallel lines have the same slope or steepness.

30. Is it possible for lines not to intersect and not be parallel either?

31. Believe it or not, this is possible.Let’s consider a 3-dimensional rectangular prism.

32. These 2 lines are not parallel, but they are not intersecting either.

33. These lines are called skew lines.

34. You might have heard the word “skewer” the last time you had a barbecue. S K E W E R

35. Lines can be… intersecting skew parallel perpendicular 90º

36. A plane is a flat surface that has length & width but no height.

37. You can see a plane only if you view it at a certain angle.

38. A true plane goes on forever in all directions.

39. A true plane goes on forever in all directions.

40. A true plane goes on forever in all directions.

41. A true plane goes on forever in all directions.

42. A true plane goes on forever in all directions.

43. 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

44. Other planes in the same figure: Any three non collinear points determine a plane! Plane AFGD Plane ACGE Plane ACH Plane AGF Plane BDG Etc.

45. 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

46. Planes can intersect.

47. Intersection of Two Planes is a Line. Plane P and Plane R intersect at the line AB B P A R

48. An X-Wing fighter from Star Wars has wings that intersect.

49. Planes can be perpendicular.

50. Planes can be parallel.