Transcript Lesson 1-1 - BakerMath.org

Lesson 1-1
Point, Line, Plane
Lesson 1-1 Point, Line, Plane
1
Definition

A postulate or axiom is an accepted
statement of fact.
Lesson 1-1 Point, Line, Plane
2
Points

Points do not have actual size.

How to Sketch:
A
Using dots

B
C
A
How to label:
Use capital letters
Never name two points with the same letter
(in the same sketch).
Lesson 1-1 Point, Line, Plane
3
Lines


Lines extend indefinitely and have no thickness or width.
How to sketch : using arrows at both ends.
n
A
B


C
How to name: 2 ways
(1) small script letter – line n
(2) any two points on the line - AB , BC, AC , BA, CA, CB
Never name a line using three points - ABC
Lesson 1-1 Point, Line, Plane
4
Postulate 1-1

Through any two points there is exactly
one line.
Lesson 1-1 Point, Line, Plane
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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
Lesson 1-1 Point, Line, Plane
Continued…….
6
Postulate 1-2

If two distinct lines intersect, then they
intersect at exactly one point.
Lesson 1-1 Point, Line, Plane
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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
A
B
C
the points on the line y = -3x + 3.
Substitute x = 1 and y = 0 in the equation.
Collinear
0 = -3 (1) + 3
C
0 = -3 + 3
A
0=0
B
The point A satisfies the equation, therefore the point is collinear
Non collinear
with the points on the line.
Lesson 1-1 Point, Line, Plane
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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
B
M
C
Horizontal Plane
Vertical Plane
Lesson 1-1 Point, Line, Plane
Other
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Postulate 1-4

Through any three noncollinear points
there is exactly one plane.
Lesson 1-1 Point, Line, Plane
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Different planes in a figure:
A
D
B
C
E
H
Plane EFGH
F
G
Plane ABCD
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc.
Lesson 1-1 Point, Line, Plane
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Other planes in the same figure:
Any three non collinear points determine a plane!
A
D
B
Plane AFGD
Plane ACGE
C
Plane ACH
E
H
F
G
Plane AGF
Plane BDG
Etc.
Lesson 1-1 Point, Line, Plane
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Coplanar Objects
Coplanar objects (points, lines, etc.) are objects that lie on
the same plane. The plane does not have to be visible.
A
D
B
C
E
H
F
G
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 ?
Lesson 1-1 Point, Line, Plane
Yes
No
Yes
Yes
Yes
No
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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
Lesson 1-1 Point, Line, Plane
Continued…….
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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
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Intersection of Two Planes is a Line.
B
P
A
R
Plane P and Plane R intersect at the line AB
Lesson 1-1 Point, Line, Plane
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Postulate 1-3

If two distinct planes intersect, then they
intersect in exactly one line.
Lesson 1-1 Point, Line, Plane
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