Segments, Rays And Angles

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A presentation for students regarding segments, rays, and angles. Also involves a 9-item quiz and exercises, as well as demonstrative techniques of "stretching" points to transform them to lines, rays, segments, and angles.

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Segments, Rays And Angles

  1. 1. One-Dimensional Euclidean Geometry
  2. 2. SPACE is the set of ALL POINTS.  A POINT is an exact place in space. It is  denoted by a dot, having no measurement nor dimension. POINTS are named using capital letters. A LINE is a stream of POINTS that doesn’t  end, and extends in both directions. LINES are named by a small letter or any two POINTS CONTAINED in the LINE.
  3. 3. l A line l or l B C line BC or line CB BC or CB
  4. 4. We can define a segment. A LINE SEGMENT  is a SUBSET/PORTION of a LINE that includes TWO POINTS and all the POINTS in BETWEEN. B C segment BC or segment CB BC or CB
  5. 5. We can define a ray. A RAY is a  SUBSET/PORTION of a LINE that includes one point called the ENDPOINT and all the POINTS on one side of the ENDPOINT. D E A RAY is a LINE SEGMENT that extends in  ONLY ONE DIRECTION.
  6. 6. D E ray DE or DE D E ray ED or ED D E line DE or line ED DE or ED
  7. 7. ALL LINES are straight.  ALL LINES and SUBSETS OF LINES are sets  of POINTS. Every SEGMENT corresponds to a unique  POSITIVE NUMBER called DISTANCE. B A 5 km 5,000 m 500 dam
  8. 8. The INTERSECTION or the place where TWO  DIFFERENT LINES meet is either ONE POINT or EVERY POINT in the line. A B C
  9. 9. 1-D Euclidean Geometry Exercise One 1. Name five . G A lines. B 2. Name five C line D H L segments. E O I 3. Name five F rays. J K
  10. 10. We can also determine a set of non-collinear  points. NON-COLLINEAR POINTS are three or more points that are not contained on the same time. COLLINEAR POINTS  lie on the same line. A From this we can  define ANGLES. B C
  11. 11. TWO NON-COLLINEAR RAYS that share the  SAME ENDPOINT form an ANGLE. The POINT where the rays intersect is called the VERTEX of the angle. The RAYS are called the SIDES of the angle. A angle ABC or ABC B angle CBA or CBA C angle B or B
  12. 12. An ACUTE ANGLE is one measuring LESS  THAN 90°. It looks more like a closed book.
  13. 13. A RIGHT ANGLE is one measuring EXACTLY  90°. It looks more like a corner.
  14. 14. An OBTUSE ANGLE is one measuring MORE  THAN 90°. It looks more like an open book.
  15. 15. 1-D Euclidean Geometry Exercise Two Name four . G A of each B type of C angle: D H L E O •acute I F •right J K •obtuse
  16. 16. Five Items True or False (45 seconds) Four Items Deductive Reasoning (20 seconds each)
  17. 17. All lines are STRAIGHT. 1. TWO NON-COLLINEAR POINTS make up 2. an angle. ALL LINES and SUBSETS OF LINES are 3. made up of points. ACUTE ANGLES look more like open books. 4. A ray is a line segment that extends in ONLY 5. ONE DIRECTION.
  18. 18. Name all the ACUTE ANGLES formed by 6. the intersection of these lines. E D A B C What are the line segments comprising the 7. ANGLE EAD?
  19. 19. If the distance AB is 5 meters, and the 8. distance BC is 20 decimeters, how many centimeters does the distance AC have, given that A-B-C? Draw angle OMG. Then, draw a line segment 9. MP such that point P is inside angle OMG.

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