1. Lesson 1-1 Point, Line, Plane

2. Lesson 1-1 Point, Line, Plane
Points
Points do not have actual size.
How to Sketch:
Using dots
How to label:
Use capital letters
Never name two points with the same letter
(in the same sketch). A B C A
Lesson 1-1 Point, Line, Plane

3. Lesson 1-1 Point, Line, Plane
Lines
Lines extend indefinitely and have no thickness or width.
How to sketch : using arrows at both ends.
How to name: 2 ways
(1) small script letter – line n
(2) any two points on the line -
Never name a line using three points - n A B C
Lesson 1-1 Point, Line, Plane

4. Lesson 1-1 Point, Line, Plane
Collinear Points
Collinear points are points that lie on the same line. (The line does not have to be visible.)
A point lies on the line if the coordinates of the point satisfy the equation of the line.
Ex: To find if A (1, 0) is collinear with
the points on the line y = -3x + 3.
Substitute x = 1 and y = 0 in the equation.
0 = -3 (1) + 3
0 =
0 = 0
The point A satisfies the equation, therefore the point is collinear
with the points on the line. A B C
Collinear C A B
Non collinear
Lesson 1-1 Point, Line, Plane

5. Lesson 1-1 Point, Line, Plane
Planes
A plane is a flat surface that extends indefinitely in all directions.
How to sketch: Use a parallelogram (four sided figure)
How to name: 2 ways
(1) Capital script letter – Plane M
(2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C
Horizontal Plane
Vertical Plane
Other
Lesson 1-1 Point, Line, Plane

6. Different planes in a figure:B
Plane ABCD
Plane EFGH
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc. D C E F H G
Lesson 1-1 Point, Line, Plane

7. Other planes in the same figure:
Any three non collinear points determine a plane!
Plane AFGD
Plane ACGE
Plane ACH
Plane AGF
Plane BDG
Etc.
Lesson 1-1 Point, Line, Plane

8. Lesson 1-1 Point, Line, Plane
Coplanar Objects
Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible.
Are the following points coplanar?
A, B, C ?
Yes
A, B, C, F ? No
H, G, F, E ?
Yes
E, H, C, B ?
Yes
A, G, F ?
Yes
C, B, F, H ? No
Lesson 1-1 Point, Line, Plane

9. Intersection of Figures
The intersection of two figures is the set of points that are common in both figures.
The intersection of two lines is a point. m
Line m and line n intersect at point P. P n
Continued…….
Lesson 1-1 Point, Line, Plane

10. 3 Possibilities of Intersection of a Line and a Plane
(1) Line passes through plane – intersection is a point.
(2) Line lies on the plane - intersection is a line.
(3) Line is parallel to the plane - no common points.
Lesson 1-1 Point, Line, Plane

11. Intersection of Two Planes is a Line.B P A R
Plane P and Plane R intersect at the line
Lesson 1-1 Point, Line, Plane

12. Lesson 1-1 Point, Line, Plane
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.
Lesson 1-1 Point, Line, Plane

13. Lesson 1-1 Point, Line, Plane
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.
Lesson 1-1 Point, Line, Plane

14. Lesson 1-1 Point, Line, Plane
Postulate 1-2
If two lines intersect they intersect in exactly one point
and intersect at C.
Lesson 1-1 Point, Line, Plane

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

16. Lesson 1-1 Point, Line, Plane
Postulate 1-4
Through any three noncollinear points there is exactly one plane.
“Think of a tripod”
Lesson 1-1 Point, Line, Plane