Geometry Fundamentals: Understanding Points, Lines, and Planes

1. Chapter 1: Basics of Geometry

2. 1-1: Patterns and Inductive Reasoning

3. conjecture an unproven statement that is based on observations

4. inductive reasoning a process that includes looking for patterns and making conjectures

5. Conjecture Information • To prove a conjecture is true, you need to prove it is true in ALL cases. • To prove a conjecture is false, provide a single counterexample. • Conjectures that are not known to be true or false are called unproven or undecided.

6. counterexample an example that shows a conjecture is false

7. Let’s Go on To the Next Section! 

8. 1-2: Points, Lines, and Planes

9. Today’s Objectives • name points, lines, segments, rays and planes • name a point that is collinear with given points • name a point that is coplanar with given points

10. definition uses known words to describe a new word

11. undefined terms a word that is not formally defined (point, line, plane) although there is general agreement about what the word means

12. point a point has no dimension and is represented by a small dot ●A point A

13. line a line extends in one dimension and is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions ● ● A BABor BA

14. Facts About Lines • is designated by 2 capital letters which represent two points on the line • may also be designated by a small letter that labels the whole line • is understood to be straight unless stated otherwise • is the shortest distance between two points

15. plane a collection of points that forms a flat surface infinitely wide and infinitely long plane M

16. collinear points points that lie on the same line segments and rays are collinear if they lie on the same line

17. coplanar points points that lie on the same plane segments, rays, and lines are coplanar if they lie on the same plane

18. line segment/segment part of a line that consists of two endpoints and all points on the line that are between the endpoints ● ● A B AB or BA

19. endpoints points at either end of a segment name segments using the endpoints

20. ray part of a line that consists of an initial point and all points on the line that extend in one direction ● ● B A BA only

21. initial point the point at the beginning of a ray when naming rays, start with the initial point

22. Question Describe what each of these symbols means: PQ PQ QP PQ

23. opposite rays if C is between A and B, then ray CA and ray CB are opposite rays ● ● ● A C B

24. Question Name two pairs of opposite rays in the figure. ● ● ● ● E F G H

25. intersect to have one or more points in common ● A

26. intersection the set of points that two or more geometric figures have in common

27. Question How can lines intersect at more than one point?

28. Question When you see a dashed line in a diagram, what does that usually imply?

29. Skill 1-2a I will name points, lines, segments, rays and planes.

30. Number 1a ●B

31. Number 2a

32. Number 3a

33. Number 4a

34. Number 5a

35. Skill 1-2b I will name a point that is collinear with given points.

36. Number 1b point D

37. Number 2b point H

38. Number 3b point G

39. Number 4b Points C and Q

40. Number 5b Points P and R

41. Number 6b Points A and Q

42. Skill 1-2c I will name a point that is coplanar with given points.

43. Number 1c point D

44. Number 2c point H

45. Number 3c Points D, E, and H

46. Number 4c Points E, F, and G

47. Number 5c Points G, H, and A

48. Let’s Do Some Homework! 

49. 1-3: Segments and Their Measures

50. Today’s Objectives • use the segment addition postulate correctly • use the distance formula to measure distances