1. Lesson 1-1 Point, Line, Plane

2. Lesson 1-1 Point, Line, Plane
Objectives
What we will learn
We will learn to identify and draw models of points, lines, and planes, and determine their characteristics.
Lesson 1-1 Point, Line, Plane

3. 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

4. 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 – AB, BC, AC
Never name a line using three points - n A B C
Lesson 1-1 Point, Line, Plane

5. Lesson 1-1 Point, Line, Plane
Line Segment
Line segments are straight and they have two endpoints.
NO arrows on both ends!
Line segments are part of a line, and come in various lengths.
Below is a picture of a line segment. When we draw one, we usually use dots to emphasize the endpoints.
Lesson 1-1 Point, Line, Plane

6. Lesson 1-1 Point, Line, Plane
Line Segment
How to name: using their endpoints. A or B
Lesson 1-1 Point, Line, Plane

7. Lesson 1-1 Point, Line, Plane
Ray
A ray is straight and it has one endpoint.
A ray extends indefinitely (forever) in one direction.
Endpoint
Lesson 1-1 Point, Line, Plane

8. Lesson 1-1 Point, Line, Plane
Ray
How to name: using its endpoint and any other point on the ray.
Note: We always write the endpoint first, then the other point. CD C D
Lesson 1-1 Point, Line, Plane

9. 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

10. 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

11. 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

12. Lesson 1-1 Point, Line, Plane
Name the planes
Front: 1) 2)
Back: 1) 2)
Top: 1) 2)
Bottom: 1) 2)
Left: 1) 2)
Right: 1) 2)
Lesson 1-1 Point, Line, Plane

13. 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

14. 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

15. Lesson 1-1 Point, Line, Plane
Postulates
Lesson 1-1 Point, Line, Plane

16. Lesson 1-1 Point, Line, Plane
Objectives: What we’ll learn…
To identify and use basic postulates about points, lines, and planes.
Lesson 1-1 Point, Line, Plane

17. Lesson 1-1 Point, Line, Plane
Definition:
Postulate (Axiom): Statements in geometry that are accepted as true.
Lesson 1-1 Point, Line, Plane

18. Lesson 1-1 Point, Line, Plane
Postulate 1-1:
Two points determine a unique line. m Q P
There is only one line that contains point P and Q.
Continued…….
Lesson 1-1 Point, Line, Plane

19. Lesson 1-1 Point, Line, Plane
Postulate 1-2:
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

20. Lesson 1-1 Point, Line, Plane
Postulate 1-3:
Three noncollinear points determine a unique plane. Ç
There is only one plane that contains points A, B , and C. B A
Continued…….
Lesson 1-1 Point, Line, Plane

21. Postulate 1.4-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

22. 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