lesson 1.2 intro to geometry. learning target i can understand basic geometric terms and postulates
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Lesson 1.2
Intro to Geometry
Learning Target
I can understand basic geometric terms and postulates.
Points Points do not have actual size.
How to Sketch:
Using dots
How to label:
Use capital letters
A
B
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 2 points on the line -
Never name a line using three points - , , , , ,AB BC AC BA CA CB
������������������������������������������������������������������������������������������������������������������������������������������������ �����������
nA
BC
ABC�������������� �
A part of a line that consists of two endpoints and all the points in between them.
How to name: by 2 endpoints
Segments
AB C
A part of a line that consists of one endpoint and all the points to one side of that endpoint.
Rays
AB C
How to name: 2 points with ENDPOINT FIRST
Not like this…
Two rays that share the same endpoint and form a straight line.
Opposite Rays
AB C
Collinear Points
A B CA
B
C
Collinear Non collinear
Collinear points are points that lie on the same line.
Coplanar Objects
Coplanar objects (points, lines, etc.) are objects that lie on the same plane.
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
Postulates
An accepted statement of fact.
Line POSTULATE – Through any two points there is exactly ONE line
AB
Planes POSTULATE – Through any 3 non-collinear points there is exactly ONE plane
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 or BCA or
BAC, etc.
A
BC
M
Different planes in a figure:A B
CD
EF
GH
Plane BCG
Plane ABF
Plane CDH
Etc.
Other planes in the same figure:
Any three non collinear points determine a plane!
H
E
G
DC
BA
F
Plane ACG
Plane ACH
Etc.
Intersection of Two Lines POSTULATE
The intersection of two lines is a point.
m
n
PLine m and line n intersect at point P.
Intersection of Two Planes POSTULATE
P
R
A
B
Plane P and Plane R intersect at the line AB�������������� �
The intersection of two planes is exactly ONE line.
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