Presentation on theme: "Geometry Sections 1.2 & 2.1 The Building Blocks of Geometry"— Presentation transcript:
1Geometry Sections 1.2 & 2.1 The Building Blocks of Geometry
2In our study of geometry, in order to avoid circular definitions, we will leave 3 terms undefined.
3point: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.
4line: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 ( ).
5plane: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 ( )
6Points are collinear if they lie on the same line.
7In 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
81) Draw an example of four collinear points 2) Draw an example of four noncollinear points
9Points are coplanar if they lie on the same plane. Points are noncoplanar if they do NOT lie on the same plane.
101)Draw an example of four coplanar points. 2) Draw an example of four noncoplanar points.
11Example: 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 ) E, F, G, A
12Just 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 isa statement that is accepted as true without proof.
13Postulate 5: Through any two points there is exactly one line. lines must be straight
14Postulate 8: Through any three noncollinear points there is exactly one Plane.
15Postulate 9: A plane contains at least 3 noncollinear points.
16Postulate 10: If two points lie in a plane then the line containing them is in the plane.
17Postulate 11: If two planes intersect, then their intersection is a line.
18A 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 ( ).
19A 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 (________).
20The intersection (symbol: ______) of two (or more) geometric figures is the set of points that are in both figures at the same time.
21Examples D A B C 1. Ray AC ray CA 2. Ray BD ray CA 3. Segment AB segment BC
22The union (symbol: ______) of two (or more) geometric figures is the set of points that are in one figure or the other or both.
23Examples D A B C 1. Line AB ray BC 2. Line segment AB line segment BC 3. Ray BD ray CA
24Example: Determine the following intersections and unions based on the figure below.
25Example: Determine the following intersections and unions based on the figure below.