1 / 17

Geometry Day 55

Geometry Day 55. Geometric Mean. Today’s Agenda. Geometric Mean Geometric Mean in Right Triangles. Geometric Mean. A Geometric Mean is a kind of average. To find the Geometric Mean between two numbers, multiply them together and take the square root.

danika
Download Presentation

Geometry Day 55

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometry Day 55 Geometric Mean

  2. Today’s Agenda • Geometric Mean • Geometric Mean in Right Triangles

  3. Geometric Mean • A Geometric Mean is a kind of average. • To find the Geometric Mean between two numbers, multiply them together and take the square root. • Example: Find the Geometric Mean of 5 and 20.

  4. Practice • Turn to p. 97 of your workbook, and try problems 1-6. • Answers:

  5. Geometric Mean as a Proportion • In a proportion if the means are equal, then that value is the geometric mean of the extremes: • x represents the Geometric Mean between a and b. • Example:

  6. Geometric Mean • This concept can used in Geometry. • One particular use is when dealing with right triangles.

  7. Geometric Mean • We start with a Right Triangle

  8. Geometric Mean • Let’s draw its altitude.

  9. Geometric Mean • We’ve now formed 2 more triangles – 3 in all! • What do these 3 triangles have in common?

  10. Geometric Mean • Let’s consider the original diagram C A B D

  11. Geometric Mean • We’ll put the others up for reference A C A A B D C D B D B C C

  12. Geometric Mean • Let’s label the sides A C A a b h d e A B c D a c a d C b h D B D B C C h e b

  13. Geometric Mean • We can use similarity properties to set up proportions: A C A a b h d e A B c D a c a d C b h D B D B C C h e b

  14. Geometric Mean • To conclude, a, b, and h, can all be written as the Geometric Mean of two segments. a b h d e c

  15. Geometric Mean • Putting it in words: • The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. • The length of this altitude is the geometric mean between the lengths of these segments. • The length of a leg of this triangle is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

  16. Example 5 20 x y z

  17. Homework 31 • Workbook, p. 98 • Word Problem Handout • If you have trouble remembering the proportions, try drawing and labeling the triangles separately. • You can confirm your answers with the Pythagorean Theorem.

More Related