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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 ) 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 D A B C 1. Ray AC ray CA 2. Ray BD ray CA**

3. Segment AB segment BC

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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 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.**

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

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Chapter 1 Section 2. Students will understand basic terms and postulates of Geometry.

Chapter 1 Section 2. Students will understand basic terms and postulates of Geometry.

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