Geometry - Points Lines Planes and Angles - Chapt 1

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Author:
Mamadams
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290720
Filename:
Geometry - Points Lines Planes and Angles - Chapt 1
Updated:
2014-12-06 18:00:04
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Geometry
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Description:
Hruska Chapter 1
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  1. Undefined terms:
    * point

    * line

    * plane
    • point - a dot, specific location

    • line - any 2 points, only 2 points, lower case cursive

    • plane - flat surface, uppercase, cursive letter, at least non-collinear
  2. Vocabulary:

    * space

    * collinear

    * coplanar

    * intersection
    space - 3 dimensional set of all points

    • collinear - points on the same line.
    • coplanar - two objects are coplanar if they lie on the same plane

    • intersection - two figures is the set of points that are in both figures.
  3. Define:

    * segment

    * ray

    * opposite rays
    • segment - part of a line including endpoints and all the point in between
    • ray - part of a line including 1 end point and all the points in one direction


    • opposite rays - two rays that:
    •   *  share endpoint
    •   *  points collinear
    •   *  rays go in opposite direction

  4. Define:

    * congruent segments

    * midpoint of a segment (midpt)

    * segment bisector (bis)
    • congruent segments - segments that have equal lengths
    • midpoint of a segment (midpt) - the point that divides the segment into two congruent segments

    • segment bisector - a segment, line or plane that intersects a segment at the midpoint.
  5. Postulate 2 

    Segment Addition Postulate

    If B is between A and C, then AB + BC = AC
  6. Angle (<) - figure formed by two rays with the same endpoint

    Parts and Naming the angle:


    Parts:
    Vertex -
    Sides -
  7. Define and draw:

    * straight angle
    * right angle
    * acute angle
    * obtuse angle
    * congruent angles
    • straight angle - measure 180°
    • right angle - measure 90°

    acute angle - measure between 0° and 90°

    obtuse angle - measure between 90° and 180°



    • congruent angles - two angles with the same measurement.
  8. Postulate 4

    Angle Addition Postulate



  9. Define:

    *  adjacent angles 
    *  angle bisector
    • adjacent angles - two coplanar angles that have:
    •   *  a common vertex
    •   *  a common side
    •   *  but NO common interior points



    angles bisector - a segment, line, ray or plane that divides the angle into two congruent adjacent angles.

  10. Postulate - a statement that describes a basic relationship between the basic terms of geometry.  It is ACCEPTED as true.

    Theorem - a statement that PROVES a conjecture is true.
  11. Postulate 5

    *  A line contains at least 2 points.
    *  A plane contains at least 3 nonlinear points
    *  Space contains at least 4 noncoplaner points.

  12. Postulate 6

    Through any 2 points there is exactly 1 line.
  13. Postulate 7

    *  Through any 3 points there is 1 plane.
    *  Through any 3 non-collinear points there is 1 plane
  14. Postulate 8

    If 2 points lie in a plane then the line contains them lies that plane.
  15. Postulate 9

    If two planes intersect, then their intersection is a line.
  16. Theorem 1-1

    If two lines intersect then do so at exactly 1 point.
  17. Theorem 1-2

    Through a line and a point not in the line there is exactly one plane.
  18. Theorem 1-3

    If two lines intersect then exactly one plane contains them.
  19. TRUE or FALSE

    1.  Two points ca lie in each of two different lines.

    2.  Three nonlinear points can lie in each of two different planes.

    3.  Three collinear point lie in only one plane.
  20. TRUE or FALSE

    1.  Two intersecting lines are contained in exactly one plane.

    2.  If two lines intersect, then they intersect in exactly one point.

    3.  If two planes intersect, then their intersection is a line.

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