Points, Lines, Planes

1. Points, Lines, Planes

3. Points Undefined term No length, width, or thickness Named with a capital letter

4. Lines Undefined term -- No thickness Length that goes on forever in two directions A straight arrangement of points

5. Plane Undefined Term Has length, width but no thickness Extends indefinitely in all directions W Plane ABC Plane W

6. The “building blocks of geometry”: • Ancient Greeks: “A point is that which has no part.” “A line is breadthless length”. • Ancient Chinese: “The line is divided into parts, and that part which has no remaining part is a point.” • Not much help, huh?

7. A definition is a statement that clarifies or explains the meaning of a word or phrase. • Unfortunately, we can’t define point, line or plane w/out using words that they themselves need defining, so… • Point, line and plane are the 3 undefined terms of geometry, yet they are the building blocks for all geometry. • IOW, using these three words, you can define all other geometric terms/figures.

8. Naming Lines

9. Intersecting LinesLines that share a point. Y n m Lines m and n intersect. Point Y is the point of intersection.

10. Perpendicular LinesTwo lines that intersect to form a right angle. r s Lines r and s intersect to form a right angle.

11. Parallel LinesLines in the same plane that do not intersect. k j Lines k an j are parallel. k || j

12. Skew LinesLines that do not lie on the same plane. (They do not intersect and are not parallel.)

13. CollinearPoints that are on the same line. C B A Points A, B and C are collinear.

14. Non-collinearPoints that are not on the same line. C B A Points A, B and C are non -collinear.

15. C B A Segment Part of a line that has two endpoints and contains all of the points in between the two endpoints.

16. Ray A part of a line consisting of one point and all points on one side of the line from that point. C B A

17. Congruent symbol Congruent Two or more figures that have the exact same size and shape.

18. C B A Midpoint A point that lies on the segment and is equal distance from each endpoint.

19. Space The set of all points.

20. Coplanar PointsPoints that lie on the same plane. Q P R Points P, Q and R are coplanar.

21. Coplanar LinesLines that lie on the same plane. x y Lines x and y are coplanar.

22. Non-Coplanar PointsPoints that do not lie on the same plane. S Q P R Points P, Q, R and S are non-coplanar.

23. Postulates/Axioms Statements that are accepted as true.

24. Theorems Statements that are proven to be true.

25. Postulate Through any 2 points there is exactly one line. B A m Line m is the only line containing both A and B

26. Postulate Every line contains at least two points. p B A Line p contains points A and B.

27. Postulate If two lines intersect, their intersection is a point. n P m Lines m and n intersect at P.

28. Postulate For any three noncollinear points, there is exactly one plane containing them. B Q C A Points A, B, and C lie in Plane Q.

29. Postulate Every plane contains at least three noncollinear points. A Y Z X Plane A contains points X, Y and Z.

30. Postulate If two planes intersect, their intersection is a line. Z k W Planes W and Z intersect in line k.

31. Postulate If two lines intersect, then they are coplanar. m n Lines m and l lie in only oneplane.

33. THE END