1
A
B
CD
1.)
From the homework, 7.3 Practice worksheet
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Do Now: Identify the similar triangles. Then find the value of x.
3
Geometric Mean
In Lesson 6.1, you learned that the geometric mean of two numbers a and b is the positive number x such that a___
xx___b=
4
Geometric Mean
Consider right ΔABC. From last class, you know that altitude CD forms two smaller triangles so that ΔCBD ~ ΔACD ~ ΔABC.
5
Leg A Leg B
Part A Part B
IHypotenuseI
Altitude
These proportions exist when a right triangle has an altitude drawn from the right angle to the hypotenuse.
6
Geometric Mean (Altitude) Theorem
altitude
altitude
other part of hypotenuse
_____________________part of hypotenuse
_____________________ =
Leg A Leg B
Part A Part B
IHypotenuseI
Altitude
Altitude as the geometric mean:
7
Use geometric mean. Find the value of y (round decimal answer to nearest tenth)
8
Use geometric mean. Find the value of x (round decimal answer to nearest tenth)
9
Use geometric mean. Find the value of b.
10
Geometric Mean (Leg) Theorem
leg
leg
part of hypotenuse_____________________
whole hypotenuse_____________________ =
Leg A Leg B
Part A Part B
IHypotenuseI
Altitude
Leg A as the geometric mean:
Leg B as the geometric mean:
11
Use geometric mean. Find the value of x.
12
Use geometric mean. Find the value of x.
13
Use geometric mean. Find the value of x, y, and z.
14
Take out your student handbook and write downthe homework assignment:
Geometric Mean worksheet
15
Geometric Mean (Altitude) Theorem
altitude
altitude
other part of hypotenuse
_____________________part of hypotenuse
_____________________ =
Leg A Leg B
Part A Part B
IHypotenuseI
Altitude
Geometric Mean (Leg) Theorem
leg
leg
part of hypotenuse_____________________
whole hypotenuse_____________________ =
Leg A Leg B
Part A Part B
IHypotenuseI
Altitude