1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label:...
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Transcript of 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label:...
![Page 1: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/1.jpg)
1
Geometric
Basics
![Page 2: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/2.jpg)
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
![Page 3: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/3.jpg)
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�������������� �
3
n
AB
C
![Page 4: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/4.jpg)
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
![Page 5: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/5.jpg)
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
![Page 6: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/6.jpg)
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.
![Page 7: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/7.jpg)
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.
![Page 8: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/8.jpg)
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
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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.
![Page 10: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/10.jpg)
Congruent SegmentsCongruent Segments
Definition:
AB
D
C
Congruent segments can be marked with dashes.
Segments with equal lengths. (congruent symbol: )
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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.
![Page 12: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/12.jpg)
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.
![Page 13: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/13.jpg)
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.
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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.
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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
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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
![Page 19: 1 Geometric Basics. Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649e605503460f94b5b99b/html5/thumbnails/19.jpg)
You Try It!
Complete Practice Problemsand check your answers with
one another.