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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, …

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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- 1. One-Dimensional Euclidean Geometry
- 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. l A line l or l B C line BC or line CB BC or CB
- 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. 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. D E ray DE or DE D E ray ED or ED D E line DE or line ED DE or ED
- 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. The INTERSECTION or the place where TWO DIFFERENT LINES meet is either ONE POINT or EVERY POINT in the line. A B C
- 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. 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. 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. An ACUTE ANGLE is one measuring LESS THAN 90°. It looks more like a closed book.
- 13. A RIGHT ANGLE is one measuring EXACTLY 90°. It looks more like a corner.
- 14. An OBTUSE ANGLE is one measuring MORE THAN 90°. It looks more like an open book.
- 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. Five Items True or False (45 seconds) Four Items Deductive Reasoning (20 seconds each)
- 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. 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. 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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