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Exploring Essential Geometry Concepts

Understand basic geometric terms and postulates - including points, lines, segments, rays, collinearity, coplanar objects, and postulates in geometry. Learn how to name and sketch various geometric elements accurately.

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Exploring Essential Geometry Concepts

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  1. Lesson 1.2 Intro to Geometry

  2. Learning Target I can understand basic geometric terms and postulates.

  3. Points • Points do not have actual size. • How to Sketch: Using dots • How to label: Use capital letters A B

  4. Lines • Lines extend indefinitely and have no thickness or width. • How to sketch : using arrows at both ends. • How to name: 2 ways (1) small script letter – line n (2) any 2points on the line - • Never name a line using three points - n A B C

  5. Segments A part of a line that consists of two endpoints and all the points in between them. How to name: by 2 endpoints A B C

  6. Rays • A part of a line that consists of one endpoint and all the points to one side of that endpoint. A B C How to name: 2 points with ENDPOINT FIRST Not like this…

  7. Opposite Rays Two rays that share the same endpoint and form a straight line. A B C

  8. Collinear Points • Collinear points are points that lie on the same line. C A A B C B Non collinear Collinear

  9. Coplanar Objects Coplanar objects (points, lines, etc.) are objects that lie on the same plane. Are the following points coplanar? A, B, C ? Yes A, B, C, F ? No H, G, F, E ? Yes E, H, C, B ? Yes A, G, F ? Yes C, B, F, H ? No

  10. Postulates • An accepted statement of fact.

  11. Line POSTULATE – Through any two points there is exactly ONE line A B

  12. Planes POSTULATE – Through any 3 non-collinear points there is exactly ONE plane • A plane is a flat surface that extends indefinitely in all directions. • How to sketch: Use a parallelogram (four sided figure) • How to name: 2 ways (1) Capital script letter – Plane M (2) Any 3 non collinear points in the plane - Plane: ABCor BCA or BAC, etc. A M B C

  13. Different planes in a figure: A B Plane BCG Plane ABF Plane CDH Etc. D C E F H G

  14. Other planes in the same figure: Any three non collinear points determine a plane! Plane ACG Plane ACH Etc.

  15. Intersection of Two Lines POSTULATE The intersection of two lines is a point. m Line m and line n intersect at point P. P n

  16. Intersection of Two Planes POSTULATE The intersection of two planes is exactly ONE line. B P A R Plane P and Plane R intersect at the line

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