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.
A segment is a part of a line with two endpoints. (NO arrows on both ends!)
Line segments come in various lengths.
Line segments are parts of lines.
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. 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

16. 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

17. 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