ac1.2apointlinesplanesbegining
DESCRIPTION
Explanation of the Meaning and Notation of the Undefined Terms of Points, Lines and Planes This is for high school studentsTRANSCRIPT
![Page 1: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/1.jpg)
Millau BridgeSir Norman Foster
Point, Lines, Planes, Angles
FallingwatersFrank Lloyd Wright
Millenium ParkFrank Lloyd Wright
Points, Lines, and PlanesBuilding Blocks of Geometry
![Page 2: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/2.jpg)
The Key Building Blocks of Geometry
Points, Lines, Planes
![Page 3: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/3.jpg)
Point
Labeled PointA
A point is thought of as a location in space without any dimension.
How come we can see it?It is only a model.
![Page 4: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/4.jpg)
Equidistant Points
• Equidistant means… the same distance away.
HG I
Point H is equidistant from point G and H.
Points G and H are equidistant from point H.
![Page 5: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/5.jpg)
Equidistant isOne of the most important concepts
in Geometry.
It is also one of the easiest.
![Page 6: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/6.jpg)
Use your compass to determine
which points are
equidistant from A.
A
B
E
F
D
C
Why ?
A, B, C,D, E
![Page 7: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/7.jpg)
A
B
E
F
D
C
![Page 8: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/8.jpg)
m AB = 10.00 cm
A B
Find a point C that is 8 cm from both A and B.
C is equidistant from A and B.
C
![Page 9: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/9.jpg)
m AB = 10.00 cm
A B
Find a point D that is also 8 cm from both A and B.
D is equidistant from A and B.
C
D
![Page 10: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/10.jpg)
A
B C
D
P
Find points equidistant from A.
Find points equidistant from B.
Find points equidistant from C.
Find points equidistant from P.
B and D
A and C
D and D
A, B, C and D
![Page 11: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/11.jpg)
Other types of PointsMain Point
Point of order
Military Point
Point of reference
Point of intersection
Peak Point
Point of No Return
Entry Point
Exit Point
Get the Point
Point it out to me.
![Page 12: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/12.jpg)
A line is thought of as a string of as consecutive points going in opposite directions.
It has no width, only length.
How come we can see it?It is only a model.
![Page 13: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/13.jpg)
A line is labeled two ways…
Or by two points on a line.
L1
By using a letter and a subscript.
A B
AB
![Page 14: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/14.jpg)
Name the line 7 different ways.
L1 A B C D
This can be a problem because their can be many alternate answers.
Lets agree to at least put the letters in alphabetical order.
![Page 15: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/15.jpg)
Name the line in different ways.
L1 A B
ABACAC
C D
L1 BCBD
CD
How many more different ways can the line be name?Use your fingers to show your answer.
7
![Page 16: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/16.jpg)
Intersecting Lines
Lines that cross each other at a point.
A
BC
D
X
![Page 17: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/17.jpg)
How many lines through 4 points?
L1 A B C D
These points are called collinear points because they are all in the same line
![Page 18: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/18.jpg)
A
B
C
Types of Points?
These points are called non-collinear points because no line can contain them all.
![Page 19: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/19.jpg)
B C D
E F
G H K
What kind of points are B, C and D?
A
Collinear
![Page 20: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/20.jpg)
B C D
E F
G H K
What kind of points are A, B and C?
A
Noncollinear
![Page 21: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/21.jpg)
B C D
E F
G H K
What kind of points are G, H and K?
A
Noncollinear
![Page 22: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/22.jpg)
B C D
E F
G H K
What kind of points are A, C, F and H?
A
collinear
![Page 23: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/23.jpg)
B C D
E F
G H K
What kind of points are A, G and K?
A
Noncollinear
![Page 24: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/24.jpg)
B C D
E F
G H K
What kind of points are G, F, and D?
A
collinear
![Page 25: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/25.jpg)
B C D
E F
G H K
What kind of points are G, H and K?
A
collinear
![Page 26: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/26.jpg)
How many lines through 4 points?
A
B
C D
3 collinear and 1 not.
4
![Page 27: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/27.jpg)
How many lines through 4 points?
A B
C D
2 collinear and 2 more collinear.
6
![Page 28: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/28.jpg)
How many lines through 4 points?
A B
C
D
No 3 points collinear.
6
![Page 29: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/29.jpg)
Other Types of Lines
Line of sight
Median Line
Line of Work
Contour Line
Boundary Line
Sailing Line
![Page 30: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/30.jpg)
Planes• Can be described as all points
that lie on a flat surface that has no edges.
• A plane extends infinitely in all directions.
![Page 31: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/31.jpg)
Planes AB
CD
Planes are named by a letter in the corner.
![Page 32: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/32.jpg)
Planes 747B
CD
Planes are named by a symbol that designates an airplane for fun.
![Page 33: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/33.jpg)
Variations of Planes
![Page 34: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/34.jpg)
H
RL
B
AA
B
A
A
Intersecting planes
![Page 35: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/35.jpg)
G
FE
D
C
H
RL
B
AA
B
A
A
The intersection of 2 planes is a line.
![Page 36: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/36.jpg)
G
FE
D
C
H
RL
B
AA
B
A
A
D is in plane…
E is in plane…
F is in plane…
C is in plane…
L
R
H
HG is in plane…
L
![Page 37: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/37.jpg)
G
FE
D
C
H
RL
B
AA
B
A
A
A is in plane…
B is in plane…All of them.
All of them.
![Page 38: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/38.jpg)
F
ED
CB
A
![Page 39: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/39.jpg)
G
A
B
C
DE
F
![Page 40: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/40.jpg)
C
S
A
D
BR
T
E
![Page 41: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/41.jpg)
H
GF
E
D
CB
A
![Page 42: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/42.jpg)
H
G
FE
D
CB
A
![Page 43: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/43.jpg)
Coplanar Points
A
B
C
![Page 44: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/44.jpg)
Space• Is the final frontier.
Is the set of all points.
It’s everywhere. It’s everywhere !!!
![Page 45: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/45.jpg)
C’est fini.
Good day and good luck.
Examples of Points, Lines, and PlaneArchitectural Examples
Following this slide.
![Page 46: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/46.jpg)
The flat surfaces are models of planes.They do not extend for ever.
Havasu Falls, Grand Canyon
![Page 47: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/47.jpg)
Floors, Lakes, Gemstones, and WaterfallsAre models of planes. They don’t extend forever.
![Page 49: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/49.jpg)
Fallingwaters by Frank Lloyd Wright
Cantilevered Planes
Bear RunWestern, PA
![Page 50: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/50.jpg)
![Page 51: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/51.jpg)
![Page 52: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/52.jpg)
![Page 53: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/53.jpg)
ColumnsDefinePlanes
![Page 54: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/54.jpg)
![Page 55: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/55.jpg)
![Page 56: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/56.jpg)
![Page 57: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/57.jpg)
![Page 58: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/58.jpg)
![Page 59: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/59.jpg)
![Page 60: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/60.jpg)
![Page 61: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/61.jpg)
![Page 62: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/62.jpg)
![Page 63: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/63.jpg)
![Page 64: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/64.jpg)
![Page 65: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/65.jpg)
![Page 66: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/66.jpg)
![Page 67: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/67.jpg)
![Page 68: Ac1.2aPointLinesPlanesBegining](https://reader035.vdocuments.us/reader035/viewer/2022062708/558b9852d8b42ade378b47a7/html5/thumbnails/68.jpg)