lesson 1-1 point, line, plane 1 lesson 1-2 point, line, plane
TRANSCRIPT
Lesson 1-1 Point, Line, Plane 1
Lesson 1-2
Point, Line, Plane
Lesson 1-1 Point, Line, Plane 2
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
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 AC
Lesson 1-1 Point, Line, Plane 4
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 -
nA
BC
ABC�������������� �
Lesson 1-1 Point, Line, Plane 5
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
Line SegmentHow to name: using their endpoints.
AB BAorB
A
Lesson 1-1 Point, Line, Plane 7
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
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.
C D CD
Lesson 1-1 Point, Line, Plane 9
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 = -3 + 3
0 = 0
The point A satisfies the equation, therefore the point is collinear
with the points on the line.
A B C
AB
C
Collinear
Non collinear
Lesson 1-1 Point, Line, Plane 10
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
BC
Horizontal Plane
M
Vertical Plane Other
Lesson 1-1 Point, Line, Plane 11
Different planes in a figure:A B
CD
EF
GH
Plane ABCD
Plane EFGH
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc.
Lesson 1-1 Point, Line, Plane 12
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!
H
E
G
DC
BA
F
Plane AFGD
Plane ACGE
Plane ACH
Plane AGF
Plane BDG
Etc.
Lesson 1-1 Point, Line, Plane 14
Coplanar Objects
Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible.
H
E
G
DC
BA
F
Are the following points coplanar?
A, B, C ?A, B, C, F ?H, G, F, E ?E, H, C, B ?A, G, F ?C, B, F, H ?
YesNo
YesYesYesNo
Lesson 1-1 Point, Line, Plane 15
Lesson 1-3
Postulates
Lesson 1-1 Point, Line, Plane 16
Objectives: What we’ll learn…
To identify and use basic postulates about points, lines, and planes.
Lesson 1-1 Point, Line, Plane 17
Definition:
Postulate (Axiom): Statements in geometry that are accepted as true.
Lesson 1-1 Point, Line, Plane 18
Postulate 1-1: Postulate 1-1:
m
P
Continued…….
There is only one line that contains point P and Q.
Q
Lesson 1-1 Point, Line, Plane 19
Postulate 1-2: Postulate 1-2:
m
n
P
Continued…….
Line m and line n intersect at point P.
Lesson 1-1 Point, Line, Plane 20
Postulate 1-3: Postulate 1-3:
Continued…….
There is only one plane that contains points A, B , and C.
Ç
B
A
Lesson 1-1 Point, Line, Plane 21
Postulate 1.4-Intersection of Two Planes is a Line.
P
R
A
B
Plane P and Plane R intersect at the line AB�������������� �
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.