geometry sections 1.2 & 2.1 the building blocks of geometry
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Geometry Sections 1.2 & 2.1 The Building Blocks of Geometry. In our study of geometry, in order to avoid circular definitions, we will leave 3 terms undefined. point :. Usually described as a dot but actually has no size. Named by a capital letter. - PowerPoint PPT PresentationTRANSCRIPT
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Geometry Sections 1.2 & 2.1The Building Blocks of Geometry
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In our study of geometry, in order to avoid circular definitions, we will
leave 3 terms undefined.
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point: Usually described as a dot but actually has no size. Named by a capital letter.
Note: When you see a capital letter in a figure, it represents a point even if the point is not drawn.
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line: A set of points that continues on without end in two opposite directions. Named by a single lower case letter ( )or any two points on the line ( ).
mor m lineBAor AB
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plane:
A set of points that extends without end in 2 dimensions. Named by a single capital letter placed in a corner ( )or by 3 points that do not all liein the same line ( )
Mor M plane
BCA plane
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Points are collinear if they lie on the same line.
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In the description of a plane, we talked about 3 points not on the
same line. Three points not on the same line are called ___________.noncollinear
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1) Draw an example of four collinear points
2) Draw an example of four noncollinear points
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Points are coplanar if they lie on the same plane.
Points are noncoplanar if they do NOT lie on the same plane.
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1)Draw an example of four coplanar points.
2) Draw an example of four noncoplanar points.
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Example: Determine if the given set of points are collinear, coplanar, both or neither.1) B, D
2) E, F, A
3) B, C, D, E
4) E, F, G, A
both
coplanar
neither
neither
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Just as undefined terms are the starting point for the vocabulary of geometry, postulates are going to be the starting point for the rules of geometry. A postulate or axiom is
a statement that is accepted as true without proof.
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Postulate 5: Through any two points there is exactly one line.
lines must be straight
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Postulate 8: Through any three noncollinear points there is exactly
one Plane.
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Postulate 9: A plane contains at least 3 noncollinear points.
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Postulate 10: If two points lie in a plane then the line containing
them is in the plane.
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Postulate 11: If two planes intersect, then their intersection is
a line.
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A line segment or segment is part of a line that begins at one point and ends at a second. Segments are named by
their two endpoints ( ).
BAor AB
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A ray is a part of a line that begins at one point and extends infinitely in one direction. Rays are named
by their endpoint and another point on the ray (________).BCor BA
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The intersection (symbol: ______) of two (or more) geometric figures is the set of points that are in both
figures at the same time.
**set of points that they SHARE**
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Examples
A B C
1. Ray AC ray CA
2. Ray BD ray CA
3. Segment AB segment BC
D
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The union (symbol: ______) of two (or more) geometric figures is the set of points that are in one figure
or the other or both.
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Examples
DA B C
1. Line AB ray BC
2. Line segment AB line segment BC
3. Ray BD ray CA
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Example: Determine the following intersections and unions based on the figure below.
DI
FH
DI
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Example: Determine the following intersections and unions based on the figure below.
F
GE