1. Lesson 8 – 1 Geometric Mean
Geometry
Lesson 8 – 1
Geometric Mean
Objective:
Find the geometric mean between two numbers.
Solve problems involving relationships between parts of a right triangle
and the altitude to its hypotenuse.

2. Geometric Mean Geometric mean Geometric mean between 9 and 4. 6
The positive square root of their product.
Geometric mean between 9 and 4. 6

3. Find the geometric mean between 8 & 10.
Simplify the radical!
What is the square root of 16?

4. Find the geometric mean
5 & 45
12 & 15
Square root of 25?
Square root of 9?
x = 5(3)
x = 15

5. Theorem
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.

6. The three triangles: FJG ~ GJH ~ FGH
Write a similarity statement identifying the three similar right triangles in the figure.
The three triangles:
FJG ~ GJH ~ FGH

7. KML ~ MPL ~ KPM STR ~ QTS ~ QSR
Write a similarity statement identifying the three similar right triangles in the figure.
KML ~ MPL ~ KPM
STR ~ QTS ~ QSR

8. Theorem Geometric Mean (Altitude) Theorem
The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments

9. Theorem 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 the length of the the hypotenuse and the segment of the hypotenuse adjacent to that leg.

10. Find x, y, and z.
x = 10
(leg theorem)

11. Find x, y, & z

12. Find x, y, and z. 16
9x = 144
x = 16
z = 15
y = 20

13. The grandstand is about 25 feet tall.
Zach wants to order a banner that will hang over the side of his high school baseball stadium grandstand and reach the ground. To find this height, he uses a cardboard square to line up the top and bottom of the grandstand. He measures his distance from the grandstand and from the ground to his eye level. Find the height of the grandstand to the nearest foot.
5.75x =
Grandstand =
The grandstand is about 25 feet tall.

14. Homework
Pg – 7 all, 8 – 24 E, – 36 EOE, 50, 54 – 74 EOE