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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. Note: When you see a capital letter in a figure, it represents a point even if the point is not drawn. line: A set of points that continues on without end in two opposite directions. Named by a single lower case letter ( line m or m )or any two points on the line ( AB or BA ). plane: A set of points that extends without end in 2 dimensions. Named by a single capital letter placed in a corner (plane M or M ) or by 3 points that do not all lie in the same line ( plane BCA ) Points are collinear if they lie on the same line. In the description of a plane, we talked about 3 points not on the same line. Three points not on the noncollinear same line are called ___________. 1) Draw an example of four collinear points 2) Draw an example of four noncollinear points Points are coplanar if they lie on the same plane. Points are noncoplanar if they do NOT lie on the same plane. 1)Draw an example of four coplanar points. 2) Draw an example of four noncoplanar points. Example: Determine if the given set of points are collinear, coplanar, both or neither. 1) B, D both 2) E, F, A coplanar 3) B, C, D, E neither 4) E, F, G, A neither 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. Postulate 5: Through any two points there is exactly one line. lines must be straight Postulate 8: Through any three noncollinear points there is exactly one Plane. Postulate 9: A plane contains at least 3 noncollinear points. Postulate 10: If two points lie in a plane then the line containing them is in the plane. Postulate 11: If two planes intersect, then their intersection is a line. 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 ( AB or BA ). 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 (________). BA or BC The intersection (symbol: ______) of two (or more) geometric figures is the set of points that are in both figures at the same time. Examples A 1. Ray AC 2. Ray BD B C 3. Segment AB D ray CA ray CA segment BC The union (symbol: ______) of two (or more) geometric figures is the set of points that are in one figure or the other or both. Examples A 1. Line AB B 2. Line segment AB 3. Ray BD D C ray BC line segment BC ray CA Example: Determine the following intersections and unions based on the figure below. DI FH DI Example: Determine the following intersections and unions based on the figure below. F GE