1. Chapter 1: Tools of Geometry
1- 3 Points, Lines, and Planes

2. Objectives, student will be able:
1. To understand basic terms of geometry.
2. To understand basic postulates of geometry.
CW/HW: pgs #’s 2 – 48 Even

3. Points How to sketch: B A How to label: C A * dots
* Use capital printed letters.
* Never label two points with
the same name (in the same sketch).
*Think of points as location markers.
*Points are zero dimensional.

4. Collinear Points Definition: Collinear points are points that lie
on the same line. (The line does not
have to be visible.)
collinear
non-collinear

5. NEVER n Lines ? ? ? How to sketch: ? How to label: ?
* must have arrows
at both ends ? ? ?
How to label: ? ? ?
(Two methods)
Possible Names:
1- small “script” letter
2- any two points on the line

6. Planes How to sketch: How to label: M * horizontal * vertical P N
horizontal “edges” M
* horizontal
* vertical P N
* other
How to label:
vertical
“edges”
(Two methods)
1- capital “script” letter
2- any three points on the plane
Think of a plane as a flat surface that has no thickness
A plane contains an infinite many lines and extends without end

7. Planes
How to label: #2- any three points on the plane

8. Planes How to label: any three points on the plane
How many planes do you see?

9. Planes How to label: any three (or more) points on the plane
How many planes do you see?
plane ABCD
plane ABC
plane BCD
plane CDA
plane DAB
etc.

10. Planes How to label: any three (or more) points on the plane
How many planes do you see?
plane EFGH
plane EFG
plane FGH
plane GHE
plane HEF
etc.

11. Planes How to label: any three (or more) points on the plane
How many planes do you see?
plane AEHD
plane EHD
plane HDA
plane DAE
plane AEH
etc.

12. Planes How to label: any three (or more) points on the plane
How many planes do you see?
plane BFGC
plane BFG
plane FGC
plane GCB
plane CBF
etc.

13. Planes How to label: any three (or more) points on the plane
How many planes do you see?
plane ABFE
plane ABF
plane BFE
plane FEA
plane EAB
etc.

14. Planes How to label: any three (or more) points on the plane
How many planes do you see?
plane DCGH
plane DCG
plane CGH
plane GHD
plane HDC
etc.

15. Planes How to label: any three (or more) points on the plane
Any three points
determine a plane!
plane AFGD
plane ACH
plane ACGE
plane AGF
plane BDG
etc.

16. Coplanar Definition: Coplanar objects (points or lines) are
objects that lie on the same plane.
(The plane does not have to be visible.)
Are they coplanar?
ABC ?
yes
ABCF ? NO
HGFE ?
yes
EHCB ?
yes
AGF ?
yes
CBFH ? NO

17. Postulate or Axiom
A postulate or axiom is an accepted statement as fact.
Postulate and Axioms have no formal proof they exist or are true
Many mathematicians do years of research trying to prove postulates or axioms true.
Postulates and axioms that are proven true are known as Theorems.

18. Postulate 1-1 Through any two points there is exactly one line.
Line t is the only line that passes through points A and B.

19. Postulate 1-2
If two lines intersect they intersect in exactly one point
and intersect at C.

20. Postulate 1-3
If two planes intersect, then they intersect in exactly one line.
Plane RST and
Plane STW
Intersect in .

21. Postulate 1-4
Through any three noncollinear points there is exactly one plane.
“Think of a tripod”

22. Space Space – the set of all points
Total space in zero dimensions is a point.
Total space in one dimension is a line.
Total space in two dimensions is a plane
Total space in three dimensions infinite in all diections