Download Lesson 8-1 Geometric Mean with answers.notebook

Lesson 8­1 Geometric Mean with answers.notebook
February 06, 2015
Questions/Main Ideas Lesson 8­1 Geometric Mean
Geometric Mean
For two positive numbers a and b, the geometric mean is the positive number x where the proportion a : x = x : b is a x
true. This proportion can be written as fractions =
x b
or with cross products x2 = ab or x = √ab
Examples
Find the geometric mean between each pair of numbers.
1. 2 and 50
2. 25 and 7
Questions/Main Ideas Theorem 8.1
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
1
Lesson 8­1 Geometric Mean with answers.notebook
February 06, 2015
Questions/Main Ideas Example 2
Write a similarity statement identifying the three similar triangles in the figure.
Questions/Main Ideas Theorem 8.2 Geometric Mean (Altitude) Theorem
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 two segments.
2
Lesson 8­1 Geometric Mean with answers.notebook
February 06, 2015
Questions/Main Ideas Theorem 8.3 Geometric Mean (Leg) Theorem
The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two 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.
Questions/Main Ideas Example 3
Find c, d, and e.
3
Lesson 8­1 Geometric Mean with answers.notebook
February 06, 2015
Questions/Main Ideas Example 4
Ms. Alspach is constructing a kite for her son. She has to arrange perpendicularly two support rods, the shorter of which is 27 inches long. If she has to place the short rod 7.25 inches from one end of the long rod in order to form two right triangle with the kite fabric, what is the length of the long rod?
4