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# Basic geometric elements

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Teaching the basic elements og geometry.

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### Basic geometric elements

1. 3. <ul><li>We may think of a point as a &quot;dot&quot; on a piece of paper. </li></ul><ul><li>We identify this point with a number or a CAPITAL letter. </li></ul><ul><li>A point has no length or width, it just specifies an exact location. </li></ul>
2. 4. <ul><li>The term intersect is used when lines, rays, line segments or figures meet, that is, they share a common point. </li></ul>IN THIS CASE THE POINT OF INTERSECTION IS D
3. 5. <ul><li>STRAIGHT LINES don’t have a beginning or an end. </li></ul><ul><li>We usually name these lines with small letters like r,s,t… </li></ul>r
4. 6. <ul><li>We may think of a ray as a straight line that begins at a certain point and extends forever in one direction. </li></ul>B
5. 7. <ul><li>It has a beginning point and an endpoint </li></ul>A B
6. 8. <ul><li>CURVED LINES </li></ul>
7. 10. r r1
8. 14. <ul><li>Two rays that share the same endpoint form an angle. </li></ul><ul><li>The point where the rays intersect is called the vertex of the angle. </li></ul><ul><li>The two rays are called the sides of the angle. </li></ul>
9. 15. <ul><li>We usually specify an angle using Greek letters like these  </li></ul><ul><li>We can also specify an angle with the letter of its vertex adding the symbol of angle like this A </li></ul>A A
10. 16. <ul><li>We measure the size of an angle using degrees. </li></ul><ul><li> </li></ul><ul><li> ACUTE < 90º </li></ul><ul><li> RIGHT= 90º </li></ul><ul><li> OBTUSE > 90º </li></ul><ul><li> FLAT = 180º </li></ul><ul><li> FULL= 360º </li></ul>CLASIFICATION BY MEASUREMENT
11. 17. <ul><li>Complementary Angles: </li></ul><ul><li>Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. </li></ul>   º 
12. 18. <ul><li>Supplementary Angles: Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. </li></ul>   º
13. 19. <ul><li>An angle bisector is a ray that divides an angle into two equal angles. </li></ul>
14. 21. <ul><li>A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. </li></ul>
15. 22. <ul><li>The figure below is not a polygon, since it is not a closed figure: </li></ul>
16. 23. <ul><li>The figure below is not a polygon, since it is not made of line segments: </li></ul>
17. 24. <ul><li>The figure below is not a polygon, since its sides do not intersect in exactly two places each: </li></ul>
18. 25. <ul><li>We’ve got two kinds of polygons: </li></ul><ul><li>REGULAR AND IRREGULAR </li></ul>examples of regular polygons examples of irregular polygons
19. 26. <ul><li>CONVEX POLYGONS: A figure is convex if every line segment drawn between any two points inside the figure lies entirely inside the figure. </li></ul>THESE FUGURES ARE CONVEX
20. 27. <ul><li>The following figures are concave. Note the red line segment drawn between two points inside the figure that also passes outside of the figure. </li></ul>Note the red line segment drawn between two points inside the figure that also passes outside the figure.
21. 29. <ul><li>The sum of the angles of a triangle is 180 degrees. </li></ul>3 SIDES (TRIANGLES) Equilateral Triangle A triangle that has three sides of equal length. The angles of an equilateral triangle all measure 60 degrees.
22. 31. <ul><li>A triangle that has three sides of different lengths. So therefore, it has three different angles. </li></ul>
23. 32. <ul><li>Acute Triangle : A triangle that has three acute angles. </li></ul>
24. 33. <ul><li>Obtuse Triangle </li></ul><ul><li>A triangle that has an obtuse angle. One of the angles of the triangle measures more than 90 degrees. </li></ul>
25. 34. <ul><li>Right Triangle </li></ul><ul><li>A triangle that has a right angle. One of the angles of the triangle measures 90 degrees. </li></ul>
26. 35. <ul><li>A four-sided polygon. The sum of the angles of a quadrilateral is 360 degrees. </li></ul>
27. 39. The radius of a circle is the distance from the center of the circle to the outside edge. RADIUS
28. 40. The diameter of a circle: The diameter of a circle is the longest distance across a circle.  (The diameter cuts through the center of the circle.  This is what makes it the longest distance.)
29. 41. (the perimeter of a circle) The circumference of a circle is the perimeter -- the distance around the outer edge. Circumference = where r = the radius of the circle and pi = 3.141592...
30. 42. A chord of a circle is a line segment that connects one point on the edge of the circle with another point on the circle. (The diameter is a chord -- it's just the longest chord!)
31. 43. An arc of a circle is a segment of the circumference of the circle.
32. 44. A sector of a circle is a pie shaped portion of the area of the circle. Technically, the piece of pie is between two segments coming out of the center of the circle.