1. Points, Lines, and Planes
The Three Undefined Terms of Geometry

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

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

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

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

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

7. A line is defined by 2 points.
Line AB

8. A ray has a starting point but no ending point.

9. A ray of light has a starting point (like the sun) and continues forever in the same direction.

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

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

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

13. A line segment also defined by 2 points.
Line Segment EF

14. Lines can do various things.

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

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

17. These angles can be right angles.
90 

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

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

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

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

22. 180  is a straight angle

23. Lines do not always intersect.

24. Lines can be parallel.

25. Parallel lines have the same slope or steepness.

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

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

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

29. These lines are called skew lines.

30. You might have heard the word “skewer” the last time you had a barbecue.
                        

31. A skewer raises your “dinner” off the surface of the grill
A skewer raises your “dinner” off the surface of the grill. The skewer does not intersect the grill, and the skewer is not parallel to the grill.

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

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

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

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

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

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

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

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

40. Planes can…

41. Planes can
intersect.

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

43. Planes can
be perpendicular.

44. Planes can
be parallel.

45. A Tie Fighter from Star Wars has wings that are parallel.

46. Planes can be…
intersecting
parallel
perpendicular

47. The end.