1. Copyright © 2005 Pearson Education, Inc. Slide 10-1

2. Copyright © 2005 Pearson Education, Inc. Chapter 10

3. Copyright © 2005 Pearson Education, Inc. Slide 10-3 Points, Lines and Planes A geometric point is imagined to have zero size. A geometric line is formed by connecting two points along the shortest possible path. Line segments are pieces of a line A geometric plane is a perfectly flat surface that has infinite length and width but no thickness. 10-A point line plane

4. Copyright © 2005 Pearson Education, Inc. Slide 10-4 Angles The intersection of two lines or line segments forms an angle. The point of intersection is called the vertex. 10-A

5. Copyright © 2005 Pearson Education, Inc. Slide 10-5 Types of Angles Right: measures 90  Straight: measures 180  Acute: measures less than 90  Obtuse: measures between 90  and 180  10-A

6. Copyright © 2005 Pearson Education, Inc. Slide 10-6 Polygons 10-A

7. Copyright © 2005 Pearson Education, Inc. Slide 10-7 Perimeter and Area 10-A

8. Copyright © 2005 Pearson Education, Inc. Slide 10-8 Surface Area and Volume 10-A

9. Copyright © 2005 Pearson Education, Inc. Slide 10-9 Platonic Solids 10-A

10. Copyright © 2005 Pearson Education, Inc. Slide 10-10 Scaling Laws Lengths always scale with the scale factor. Areas always scale with the square of the scale factor. Volumes always scale with the cube of the scale factor. 10-A

11. Copyright © 2005 Pearson Education, Inc. Slide 10-11 Pythagorean Theorem The Pythagorean theorem applies only to right triangle (those with one 90  angle). For a right triangle with side lengths a, b, and c, in which c is the longest side (or hypotenuse), the Pythagorean theorem states that a 2 + b 2 = c 2 10-B a b c

12. Copyright © 2005 Pearson Education, Inc. Slide 10-12 Similar Triangles 10-B

13. Copyright © 2005 Pearson Education, Inc. Slide 10-13 Snowflake Curve & Fractal Dimension 10-C The fractal dimension of an object is defined as a number D such that N = R D where N is the factor by which the number of elements increases when we shorten the ruler by a reduction factor R.

14. Copyright © 2005 Pearson Education, Inc. Slide 10-14 Sierpinksi Triangle Iterations 10-C

15. Copyright © 2005 Pearson Education, Inc. Slide 10-15 Sierpinksi Triangle Iterations 10-C

16. Copyright © 2005 Pearson Education, Inc. Slide 10-16 Sierpinksi Triangle Iterations 10-C

17. Copyright © 2005 Pearson Education, Inc. Slide 10-17 Sierpinksi Triangle Iterations 10-C

18. Copyright © 2005 Pearson Education, Inc. Slide 10-18 The Mandelbrot Set 10-C

19. Copyright © 2005 Pearson Education, Inc. Slide 10-19 Two Views of Barnsley’s Fern 10-C

20. Copyright © 2005 Pearson Education, Inc. Slide 10-20 A Fractal Landscape by Anne Burns 10-C