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Some Basic Figures

Some Basic Figures. Points, Lines, Planes, and Angles. Objectives. Definitions and Postulates. Geometry. Segments, Rays, and Distance. Segment- Ray - Opposite Rays- Length of a segment- distance between the two endpoints. Vocabulary.

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Some Basic Figures

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  1. Some Basic Figures Points, Lines, Planes, and Angles

  2. Objectives

  3. Definitions and Postulates Geometry

  4. Segments, Rays, and Distance Segment- Ray - Opposite Rays- Length of a segment- distance between the two endpoints

  5. Vocabulary Congruent- two shapes that have the same size and shape. Congruent Segments-segments that have equal lengths Midpoint of a segment-the point that divides the segment into two congruent segments. Bisector of a segment- a line, segment, ray, or plane that intersects the segment at its midpoint.

  6. Postulate 1 (Ruler Postulate) Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates.

  7. Postulate 2 (Segment Addition Postulate) If B is between A and C, then AB + BC = AC A C B

  8. Angles Geometry

  9. Postulates and Theorems Relating Points, Lines and Planes

  10. Vocabulary • Congruent Angles-angles that have equal measures • Adjacent Angles-two angles in a plane that have common vertex and a common side but no common interior points.

  11. Vocabulary • Bisector of an angle- the ray that divides that angle into two congruent adjacent angle.

  12. Postulate 3 (Protractor Postulate)

  13. Postulate 4 (Angle Addition Postulate)

  14. Postulate 5 A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane.

  15. Postulate 6 • Through any two points there is exactly one line.

  16. Postulate 7 • Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.

  17. Postulate 8 • If two points are in a plane, then the line that contains the points is in that plane.

  18. Postulate 9 • If two planes intersect, then their intersection is a line.

  19. Theorems Theorem 1 If two lines intersect, then they intersect in exactly one point. Theorem 2 Through a line and a point not in the line there is exactly one plane Theorem 3 If two lines intersect, then exactly one plane contains the lines

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