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Geometry Sections 1.2 & 2.1 The 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 ( ).

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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 lie in the same line ( )

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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

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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 ( ).

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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 (________).

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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.

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Examples AB C 1. Ray AC ray CA 2. Ray BDray CA 3. Segment ABsegment 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 D A BC 1. Line ABray BC 2. Line segment AB line segment BC 3. Ray BDray CA

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Example: Determine the following intersections and unions based on the figure below.

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