basics of geometry 2013.ppt
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Transcript of basics of geometry 2013.ppt
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Basics of Geometry
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Basics of Geometry
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Basics of Geometry
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Basics of Geometry
Basics of Geometry
POINTS!
LINES!
PLANES!
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Basics of Geometry
The terms points, lines, and planes are the foundations ofgeometry, but
point, line, and plane are all what we call undefined terms.
Undefined Terms?
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Basics of Geometry
Has no dimension Denotes or represents a position or location
Usually represented by a small dot
Point
A
The above is called point A ( A). Note the
point is represented with a capital letter.
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Basics of Geometry
Has one dimension (length)
Extends indefinitely in both directions without end
Represented with straight line with two arrowheads to
indicate that the line extends without end in two directions.
Line
l
B
A
This is Line l, (using the lower case script
letter) or symbolically we call it .AB
NOTICE: The arrowheads are in
both directions on the symbol
AB
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Basics of Geometry
Plane Extend in two dimensions.
Represented by a slanted 4 sided figure, but you
must envision it extends without end, even
though the representation has edges.
A
B CM This is Plane Mor plane ABC
(be sure to only use three of the
points when naming a plane)
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Basics of Geometry
Undefined Concepts
Collinear points are points that lie on the
same line.
l
C
AB Points A, B and C are collinear.
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Basics of Geometry
Undefined Concepts
Coplanar points are points that lie on the
same plane.
A
BC Points A, B and C are coplanar.
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Basics of Geometry
Line Segment
Here is line AB, or recall
symbolicallyAB
A B
The line segment does not
extend or without end. It has
endpoints, in this case A and
B. The segment contains all
the points on the line
between A and B
A B
Notice the difference in
the symbol!
This is segment AB
It is a part of a line or subset of a line.
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Basics of Geometry
Symbolized by
Ray
AB
The initial point isalways the first
letter in naming a
ray. Notice the
difference in
symbols from both
a line and segment.
A B
A is called the initial
point
Ray AB extends in
one direction
without end.
Lets look at a ray:
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Basics of Geometry
Not all symbols are created equal!
Symbol alert!
BAAB is the same as
AB BAis the same as
BUT
A B
A B
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Basics of Geometry
AB is not the same as BA
Symbol alert!!
A B AB
A B BA
Initial point 1stThe ray is different!
Notice that the initial point is listed first in the symbol. Also note
that the symbolic ray always has the arrowhead on the right
regardless of the direction of the ray.
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Basics of Geometry
Name the geometric concept represented by each.
Quick Quiz!!!
1. tip of a pen
2. top of a table
3. edge of a computer table
4. head of pin
5. wire
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Basics of Geometry
Name the geometric concept represented by each.
Quick Quiz!!!
6. clothesline
7. train track
8. chalkboard
9. shoe laces
10. beam of light
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Basics of Geometry
Quick Quiz !!!!1. Name 3 points that are collinear.
Points D, F and B lie on the same line, therefore they are collinear.
2. Name 4 points that are coplanar.
If you answered D, F, B, and G are coplanar, then you are correct. It is
harder to see because the plane is not drawn, but points D, F, B and M
are also coplanar.
3. Name 3 points that are not collinear.
There are many correct answers, D, F, M are not
collinear.
M
G
DF
B