Lesson 1-1 Point, Line, Plane 1 Point, Line, Plane
Jan 23, 2016
Lesson 1-1 Point, Line, Plane 1
Point, Line, Plane
Point – a specific location in space 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).
Lesson 1-1 Point, Line, Plane 2
A
B AC
Line- segment extending forever in opposite directions Lines extend indefinitely and have no thickness or width. How to sketch : using arrows at both ends.
How to name: several ways(1) small script letter – line n or n(2) any two points on the line -
Never name a line using three points – 2 points make up a line
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Lesson 1-1 Point, Line, Plane 3
n AB
C
A plane is a flat surface that extends indefinitely in all directions. How to sketch: Use a parallelogram (four sided figure) How to name: 3 ways(1) Capital script letter – Plane M, M, Plane ABC(2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC /
BCA / CAB / CBA
Lesson 1-1 Point, Line, Plane 4
A
BC
Horizontal Plane
M
Vertical Plane Other
Lesson 1-1 Point, Line, Plane 5
A B
CD
EF
GH
Plane ABCD
Plane EFGH
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc.
Any three non collinear points determine a plane!
Lesson 1-1 Point, Line, Plane 6
H
E
G
DC
BA
F
Plane AFGD
Plane ACGE
Plane ACH
Plane AGF
Plane BDG
Etc.
Coplanar objects (points, lines, etc.) are objects could be on the same plane. The plane does not have to be visible.
Lesson 1-1 Point, Line, Plane 7
H
E
G
DC
BA
F
Are the following points coplanar?
A, B, C ?
H, G, F, E ?
E, H, C, B ?A, G, F ?
Yes
Yes
YesYes
Points that could not be connected by a plane are said to be Non Coplanar
pointsA C B FB C E G
Lesson 1-1 Point, Line, Plane 8
H
E
G
DC
BA
F
NO
NO
The intersection of two figures is the list of all points that are shared by both figures.
Lesson 1-1 Point, Line, Plane 9
The intersection of two lines is a point.
m
n
P
Continued…….
Line m and line n intersect at point P.
(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 10
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.
Lesson 1-1 Point, Line, Plane 11
A B C AB
C
Collinear
Non collinear
Noncollinear points are points that do no lie on the same line.
Lesson 1-1 Point, Line, Plane 12
A
B
C
Non collinear
Lesson 1-1 Point, Line, Plane 13
III
III IVORIG
IN
X-Axis
Y-Axis
Lesson 1-2: Segments and Rays 14
Definition: An assumption that needs no explanation.
Examples:
• Through any two points there is exactly one line.
• Through any three points, there is exactly one plane.
• A line contains at least two points.
• A plane contains at least three non collinear points.
Postulate #1
Postulate #3
Postulate #2
Postulate #1
Lesson 1-2: Segments and Rays 15
• If two planes intersect, then the intersecting is a line.
• If two points lie in a plane, then the line containing the two points lie in the same plane.
Examples:
Lesson 1-2: Segments and Rays 16
Postulate #7: If 2 lines intersect then their intersection is exactly
What is a Theorem?
ONE POINT
A theorem is a statement that can be PROVEN true.