Post on 28-Dec-2015
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Geometric
Basics
PointsPoints• 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.
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A
BA
LinesLines• 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������������������������������������������������������������������������������������������������������������������������������������������������ �����������
ABC�������������� �
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n
AB
C
Collinear PointsCollinear Points
• Lie on the same line. (The line does not have to be visible).
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A B C
A
B
C
Collinear
Non collinear
PlanesPlanes• 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
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A
BC
Horizontal Plane
M
Vertical Plane Other
Different planes in a Different planes in a figure:figure:
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A B
CD
EF
GH
Plane ABCD
Plane EFGH
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc.
Other planes in the same Other planes in the same figure:figure:
Any three non collinear points determine a plane!
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H
E
G
DC
BA
F
Plane AFGD
Plane ACGE
Plane ACH
Plane AGF
Plane BDG
Etc.
Coplanar ObjectsCoplanar Objects
Coplanar objects (points, lines, etc.) lie on the same plane. The plane does not have to be visible.
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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 ?
Yes
No
Yes
Yes
Yes
No
SegmentSegment
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Part of a line that consists of two points called the endpoints and all points between them.
How to sketch:
How to name:
Definition:
AB
AB or BA
The symbol AB is read as "segment AB".
AB (without a symbol) means the length of the segment or the distance between points A and B.
Congruent SegmentsCongruent Segments
Definition:
AB
D
C
Congruent segments can be marked with dashes.
Segments with equal lengths. (congruent symbol: )
RayRay
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Definition:
( the symbol RA is read as “ray RA” )
How to sketch:
How to name:
R
A R A Y
RA ( not AR ) RA or RY ( not RAY )
RA : RA and all points Y such that A is between R and Y.
Opposite RaysOpposite Rays
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Definition:
( Opposite rays must have the same “endpoint” )
AX Y
D ED E
opposite rays not opposite rays
DE and ED are not opposite rays.
If A is between X and Y, AX and AY are opposite rays.
Intersection of FiguresIntersection of Figures
The intersection of two figures is the set of points that are common in both figures.
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The intersection of two lines is a point.
m
n
P
Line m and line n intersect at point P.
3 Possibilities of Intersection of a3 Possibilities of Intersection of aLine and a PlaneLine 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.
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Intersection of Two Planes Intersection of Two Planes is a Line.is a Line.
AB�������������� �
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P
R
A
B
Plane P and Plane R intersect at the line
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Segment BisectorsSegment Bisectors
Any segment, line or plane that divides a segment into two congruent parts is called segment bisector.
Definition:
B
E
D
FA
BE
D
FA
E
D
A F
B
AB bisects DF. AB bisects DF.
AB bisects DF.Plane M bisects DF.
BetweenBetween
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Definition: X is between A and B if AX + XB = AB.
A BX
AX + XB = AB AX + XB > AB
A BX
The Segment Addition The Segment Addition PostulatePostulate
AB
C
If C is between A and B, then AC + CB = AB.
Postulate:
Example: If AC = x , CB = 2x and AB = 12, then, find x, AC and CB.
AC + CB = AB
x + 2x = 12
3x = 12
x = 4
2xx
12
x = 4AC = 4CB = 8
Step 1: Draw a figure
Step 2: Label fig. with given info.
Step 3: Write an equation
Step 4: Solve and find all the answers
You Try It!
Complete Practice Problemsand check your answers with
one another.