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• Geometry as we know it today was first developed by Greeks who lived in what is now Egypt.

Explore the history of geometry and learn about the fundamental concepts of points, lines, and planes. Discover the significance of collinear and coplanar points and delve into the basic postulates that form the foundation of geometry.

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• Geometry as we know it today was first developed by Greeks who lived in what is now Egypt.

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  1. •Geometry is by far the oldest branch of mathematics.• Every ancient civilization developed some form of geometry, as a way of helping withsurvival.

  2. •Geometry as we know it today was first developed by Greeks who lived in what is now Egypt.

  3. •Geometry was formally organized by the mathematician Euclid in a book called The Elementsaround 300 B.C.

  4. •Every geometry book for the past 2,300 years has been based on Euclid’s Elements.

  5. Geometry• literally means “earth measure”• study of shapes and their relationships

  6. Main “building blocks” of geometry

  7. •point • a location, usually represented by a dot • points are infinitely small • no length, width, or thickness • 0 dimensions

  8. • We typically represent points with dots and name them with capital letters.

  9. • line • shortest path from one point to another • infinitely thin; no thickness• extends forever in opposite directions • 1 dimension

  10. •Usually named by two points that form it.

  11. •Lines are named with TWO points (not 3 or more)•You put a line symbol (double arrow) above the name of a line.

  12. •Lines can also be named with small cursive (or italic) letters. These are lines l and m .

  13. Give as many names for this line as you can.

  14. • plane

  15. • plane

  16. • plane •flat surface with no thickness and no boundaries•extends forever, but infinitely thin•2 dimensions

  17. •We most often show planes by drawing a parallelogram (or other four-sided shapes)

  18. •Planes are often names with capital, cursive letters.

  19. •You can also name a plane with three points that are on it, like ABC.

  20. In most cases we will just consider single planes, but we can also talk about•space •all the possible points in 3 dimensions

  21. Collinear on the same lineCoplanar on the same plane

  22. Parts of lines

  23. • Segment •Connects two points •Stops at the endpoints•Named by putting a bar above the endpoints

  24. • Ray •Extends endlessly in one direction •Starts at an endpoint and continues.

  25. • Named with an endpoint and one other point on the ray, with an arrow above them.(The first letter must be the endpoint.)

  26. • Opposite rays •Share the same endpoint •Together make a line

  27. Postulate A statement that is so obvious we assume it is true without questioning it.

  28.  We use postulates toexplain why other things aretrue.

  29.  Euclid built all of geometry from just 5 postulates.We’ll use a lot more, 4 of which we’ll learn today.

  30.  Through any 2 points there is exactly 1 line.

  31.  If 2 lines intersect, the intersection is a point.

  32.  Through any 3noncollinearpoints thereis exactly 1 plane.

  33.  If 2 planes intersect, the intersection is a line.

  34. Know … History of geometry Point, line, plane, space Collinear, coplanar Segment, ray, opposite rays Postulate 4 basic postulates of points, lines, & planes

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