Download presentation

Presentation is loading. Please wait.

1
Slide #1

2
**8.1 Geometric Mean and Pythagorean Theorem**

Geometry

3
**Objectives/Assignment**

Use Pythagorean theorem to solve problems Use Geometric Mean and Pythagorean Theorem to solve real-life problems

4
Geometric Mean The geometric mean of two positive numbers a and b is the positive number x such that a x If you solve this proportion for x, you find that x = √a ∙ b which is a positive number. = x b

5
Book Example Pg 397

6
**Geometric Mean Example**

For example, the geometric mean of 8 and 18 is 12, because 8 12 = 12 18 and also because x = √8 ∙ 18 = x = √144 = 12

7
**Practice “Geometric Mean”**

8
Geometric mean PAPER SIZES. International standard paper sizes are commonly used all over the world. The various sizes all have the same width-to-length ratios. Two sizes of paper are shown, called A4 and A3. The distance labeled x is the geometric mean of 210 mm and 420 mm. Find the value of x.

9
**Write proportion 210 x = x 420 X2 = 210 ∙ 420 X = √210 ∙ 420 X = 297mm**

Solution: 210 x Write proportion = x 420 X2 = 210 ∙ 420 X = √210 ∙ 420 X = 297mm Cross product property Simplify

11
**Find the positive square root.**

EXAMPLE 1 Find the length of a hypotenuse Find the length of the hypotenuse of the right triangle. (hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem x2 = Substitute. x2 = Square. x2 = 100 Add. x = 10 Find the positive square root.

12
GUIDED PRACTICE for Example 1 1. Find the unknown side length of the right triangle. Write your answer in simplest radical form. ANSWER 4

13
GUIDED PRACTICE for Example 1 Find the unknown side length of the right triangle. 2. 13 ANSWER

15
X = 3.2 Y = X + 5 Y = Y = 8.2

16
5.7²+ 8² = x² = x² 96.49 = x² X = 9.8 Y² = 32 Y = 5.7

17
x 4 4.5²+ 5² = y² = y² 45 = y² X = 6.7 x² = 20 x = 4.5

18
x² = 18 x = 4.2 6²+ 4.2² = y² = y² 54 = y² X = 7.3

19
x²+ 5² = 9² x² + 25 = 81 x² = 81-25 X² = 56 X = 7.5

20
2²+ 2² = x² 4 + 4 = x² x² = 8 X = 2.8

21
30²+ 16² = x² = x² x² = 1156 X = 34

22
x+ 60² = 65² x² = 4225 x² = x² = 625 X = 25

23
14² + 48² = 50² 50² + 75² = 85² 15² + 36² = 39² 45² + 60² = 80² ?

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google