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Lesson 1-1 Point, Line, Plane 1
Lesson 1-3
Point, Line, Plane
Lesson 1-1 Point, Line, Plane 2
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 3
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 -
Never name a line using three points - , , , , ,AB BC AC BA CA CB
������������������������������������������������������������������������������������������������������������������������������������������������ �����������
nA
BC
ABC�������������� �
Lesson 1-1 Point, Line, Plane 4
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 5
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 6
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 7
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 8
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 9
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
n
P
Continued…….
Line m and line n intersect at point P.
Lesson 1-1 Point, Line, Plane 10
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 11
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 12
Postulate or Axiom
A postulate or axiom is an accepted statement as fact.
Postulate and Axioms have no formal proof they exist or are true
Many mathematicians do years of research trying to prove postulates or axioms true.
Postulates and axioms that are proven true are known as Theorems.
Lesson 1-1 Point, Line, Plane 13
Postulate 1-1 Through any two points there is exactly
one line.
Line t is the only line that passes through points A and B.
Lesson 1-1 Point, Line, Plane 14
Postulate 1-2
If two lines intersect they intersect in exactly one point
and intersect at C. AE BD
Lesson 1-1 Point, Line, Plane 15
Postulate 1-3
If two planes intersect, then they intersect in exactly one line.
Plane RST and Plane STW Intersect in .
AE
AE
ST
Lesson 1-1 Point, Line, Plane 16
Postulate 1-4
Through any three noncollinear points there is exactly one plane.
“Think of a tripod”
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