Ac1.2aPointLinesPlanesBegining
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Millau BridgeSir Norman Foster
Point, Lines, Planes, Angles
FallingwatersFrank Lloyd Wright
Millenium ParkFrank Lloyd Wright
Points, Lines, and PlanesBuilding Blocks of Geometry
The Key Building Blocks of Geometry
Points, Lines, Planes
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.
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.
Equidistant isOne of the most important concepts
in Geometry.
It is also one of the easiest.
Use your compass to determine
which points are
equidistant from A.
A
B
E
F
D
C
Why ?
A, B, C,D, E
A
B
E
F
D
C
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
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
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
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.
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.
A line is labeled two ways…
Or by two points on a line.
L1
By using a letter and a subscript.
A B
AB
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.
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
Intersecting Lines
Lines that cross each other at a point.
A
BC
D
X
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
A
B
C
Types of Points?
These points are called non-collinear points because no line can contain them all.
B C D
E F
G H K
What kind of points are B, C and D?
A
Collinear
B C D
E F
G H K
What kind of points are A, B and C?
A
Noncollinear
B C D
E F
G H K
What kind of points are G, H and K?
A
Noncollinear
B C D
E F
G H K
What kind of points are A, C, F and H?
A
collinear
B C D
E F
G H K
What kind of points are A, G and K?
A
Noncollinear
B C D
E F
G H K
What kind of points are G, F, and D?
A
collinear
B C D
E F
G H K
What kind of points are G, H and K?
A
collinear
How many lines through 4 points?
A
B
C D
3 collinear and 1 not.
4
How many lines through 4 points?
A B
C D
2 collinear and 2 more collinear.
6
How many lines through 4 points?
A B
C
D
No 3 points collinear.
6
Other Types of Lines
Line of sight
Median Line
Line of Work
Contour Line
Boundary Line
Sailing Line
Planes• Can be described as all points
that lie on a flat surface that has no edges.
• A plane extends infinitely in all directions.
Planes AB
CD
Planes are named by a letter in the corner.
Planes 747B
CD
Planes are named by a symbol that designates an airplane for fun.
Variations of Planes
H
RL
B
AA
B
A
A
Intersecting planes
G
FE
D
C
H
RL
B
AA
B
A
A
The intersection of 2 planes is a line.
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
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.
F
ED
CB
A
G
A
B
C
DE
F
C
S
A
D
BR
T
E
H
GF
E
D
CB
A
H
G
FE
D
CB
A
Coplanar Points
A
B
C
Space• Is the final frontier.
Is the set of all points.
It’s everywhere. It’s everywhere !!!
C’est fini.
Good day and good luck.
Examples of Points, Lines, and PlaneArchitectural Examples
Following this slide.
The flat surfaces are models of planes.They do not extend for ever.
Havasu Falls, Grand Canyon
Floors, Lakes, Gemstones, and WaterfallsAre models of planes. They don’t extend forever.
Fallingwaters by Frank Lloyd Wright
Cantilevered Planes
Bear RunWestern, PA
ColumnsDefinePlanes