Similar Right Triangles Thm.
If the altitude is drawn to the hypotenuse of a
right triangle, then the two triangles formed
are similar to the original triangle and each
other.
A
∆ABC ~ ∆BDC ~ ∆ADB
D
B
C
∆ABC ~ ∆BDC ~ ∆ADB
A
D
A
B
B
C
C
∆ABC ~ ∆BDC ~ ∆ADB
A
A
C
B
B
D
D
C
B
Identify the similar triangles. Then find the
value of x.
G
5
4
E
H
x
3
F
Find the geometric mean. Put your
answer in simplest radical form
8 and 17
11 and 3
Geometric Mean
Geometric mean (x) of "a" and "b" is:
Satisfies the proportion:
x
a
__
__
=
x
b
5 and 30
Geometric Mean - Altitude Thm.
In a right triangle, the altitude from the right angle to the
hypotenuse divides the hypotenuse into two segments.
The length of the altitude is the geometric mean of these
two segments
x
z
=
z
y
x
y
z
z2 = xy
Geometric Mean - Leg Thm.
In a right triangle, the altitude from the right angle to the
hypotenuse divides the hypotenuse into two segments.
The length of each leg of the large right triangle is
geometric mean of the hypotenuse and segment of the
hypotenuse adjacent to the leg
z
x+w
z = x
w
y
x
z
so
y
x+w
y = w
so
Find the value of x, y, and z
z
y
x
3
7