Explanation of the Meaning and Notation of the Undefined Terms of Points, Lines and Planes This is for high school students

1. Millau Bridge Sir Norman Foster Point, Lines, Planes, Angles Fallingwaters Frank Lloyd Wright Millenium Park Frank Lloyd Wright Points, Lines, and Planes Building Blocks of Geometry

2. Points, Lines, Planes The Key Building Blocks of Geometry

3. Point Labeled Point A A point is thought of as a location in space without any dimension. How come we can see it? It is only a model.

5. Equidistant is One of the most important concepts in Geometry . It is also one of the easiest.

6. Use your compass to determine which points are equidistant from A. Why ? A, B, C, D, E

8. Find a point C that is 8 cm from both A and B. C is equidistant from A and B. C

9. Find a point D that is also 8 cm from both A and B. D is equidistant from A and B. C D

10. A B C D P Find points equidistant from A. Find points equidistant from B. Find points equidistant from C. Find points equidistant from P. B and D A and C D and D A, B, C and D

11. Other types of Points Main Point Point of order Military Point Point of reference Point of intersection Peak Point Point of No Return Entry Point Exit Point Get the Point Point it out to me.

12. A line is thought of as a string of as consecutive points going in opposite directions. It has no width, only length. How come we can see it? It is only a model.

13. A line is labeled two ways… Or by two points on a line. L 1 By using a letter and a subscript. A B AB

14. Name the line 7 different ways. L 1 A B C D This can be a problem because their can be many alternate answers. Lets agree to at least put the letters in alphabetical order.

15. Name the line in different ways. L 1 A B AB AC AC C D L 1 BC BD CD How many more different ways can the line be name? Use your fingers to show your answer. 7

16. Intersecting Lines Lines that cross each other at a point. A B C D X

17. How many lines through 4 points? L 1 A B C D These points are called collinear points because they are all in the same line

18. Types of Points? These points are called non-collinear points because no line can contain them all.

19. B C D E F G H K What kind of points are B, C and D? A Collinear

20. B C D E F G H K What kind of points are A, B and C? A Noncollinear

21. B C D E F G H K What kind of points are G, H and K? A Noncollinear

22. B C D E F G H K What kind of points are A, C, F and H? A collinear

23. B C D E F G H K What kind of points are A, G and K? A Noncollinear

24. B C D E F G H K What kind of points are G, F, and D? A collinear

25. B C D E F G H K What kind of points are G, H and K? A collinear

26. How many lines through 4 points? A B C D 3 collinear and 1 not. 4

27. How many lines through 4 points? A B C D 2 collinear and 2 more collinear. 6

28. How many lines through 4 points? A B C D No 3 points collinear. 6

29. Other Types of Lines Line of sight Median Line Line of Work Contour Line Boundary Line Sailing Line

31. Planes A B C D Planes are named by a letter in the corner.

32. Planes 747 B C D Planes are named by a symbol that designates an airplane for fun.

33. Variations of Planes

34. Intersecting planes

35. The intersection of 2 planes is a line.

36. D is in plane… E is in plane… F is in plane… C is in plane… L R H H G is in plane… L

37. A is in plane… B is in plane… All of them. All of them.

43. Coplanar Points

45. C’est fini. Good day and good luck. Examples of Points, Lines, and Plane Architectural Examples Following this slide.

46. The flat surfaces are models of planes. They do not extend for ever. Havasu Falls, Grand Canyon

47. Floors, Lakes, Gemstones, and Waterfalls Are models of planes. They don’t extend forever.

48. Cascading planes of rice patties. Asia

49. Fallingwaters by Frank Lloyd Wright Cantilevered Planes Bear Run Western, PA

53. Columns Define Planes