Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Find Geometric Means and Segment Lengths in Similar Right Triangles
1. Obj. 39 Similar Right Triangles
The student is able to (I can):
• Use geometric mean to find segment lengths in right
triangles
• Apply similarity relationships in right triangles to solve
problems.
2. geometric
mean
A proportion with the following pattern:
a x
=
x b
or x 2 = ab
or
x = ab
Example: Find the geometric mean of 5 and
20.
5
x
=
x 20
x 2 = 100
x = 10
3. Thm 8-1-1
The altitude to the hypotenuse of a right
triangle forms two triangles that are
similar to each other and to the original
I
triangle.
90˚-∠M
90˚-∠M
M
T
E
M
M
T
I
E
I
T
E
I
∆MIT ~ ∆IET ~ ∆MEI
4. Because the triangles are similar, we can
set up proportions between the sides:
MI IE ME
=
=
, etc.
I
IT ET EI
M
T
E
M
M
T
I
E
I
T
E
I
∆MIT ~ ∆IET ~ ∆MEI
5. Cor. 8-1-2
The length of the altitude to the
hypotenuse is the geometric mean of the
lengths of the two segments.
E
b
H
h
T x A
y
c
x h
=
h y
or
a
h2 = xy
6. Cor. 8-1-3
The length of a leg of a right triangle is the
geometric mean of the lengths of the
hypotenuse and the segment of the
hypotenuse adjacent to that leg.
E
b
H
h
a
T x A
y
c
x a
=
a c
or
a2 = xc
y b
=
b c
or
b 2 = yc
7. When you are setting up these problems,
remember you are basically setting up
similar triangles.
Example
1. Find x, y, and z.
x
6
9
y
z
9 6
=
6 x
9x = 36
x=4
9
z
=
z 9+4
z 2 = 117
z = 3 13
4
y
=
y 9+4
y 2 = 52
y = 2 13