Download Lesson 7-4: Geometric Mean Arithmetic Mean vs. Geometric Mean

Geometry NOTES
Date: ________
Lesson 7-4: Geometric Mean
Arithmetic Mean

Add the numbers

Divide by the total number of numbers
Ex: find the mean between 3 and 5
vs.
Geometric Mean
* If “a” and “b” are positive numbers,
then “g” is the geometric mean if
a g

g b
Ex: find the geometric mean between
3 and 5.
Corollary #1: IF the altitude is drawn to the hypotenuse of a right triangle, then the ALTITUDE
is the geometric mean between the two segments of the hypotenuse.
1st piece of hypotenuse
altitude

altitude
2nd piece of hypotenuse
Solve for x:
6.
7.
9. If CD = 4, and AD = 2, find DB.
11. If CD = 8, and AD = DB, find AB.
8.
10.
If AD = 5, AB = 17, find CD.
Corollary #2: If the altitude is drawn to the hypotenuse in a right triangle, then the LEG is the
geometric mean between the entire hypotenuse and the piece of the hypotenuse that is adjacent to
the leg.
entire hypotenuse
leg

leg
piece of hypotenuse
Solve for x:
12.
13.
14.
15.
Use both corollaries to solve for x and y:
16.
18.
HOMEWORK: Practice Worksheet 7.4 A
17.