Transcript Geometry Section 7.3

Geometry
Section 7.3
Use Similar Right Triangles
Theorem
• 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.
Examples
• Identify the similar triangles then find the
value of x.
L
B
D
3
13 K
5
12
x
A
x
J
A
C
4
55
M
Geometric Mean (Altitude)
Theorem
• 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 the lengths of the
two segments.
Geometric Mean (Leg) Theorem
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 right triangle is the
geometric mean of the
lengths of the hypotenuse
and the segment of the
hypotenuse that is
adjacent to the leg.
Examples
• Find the length of the variable using the
geometric mean theorems.
8
5
8
x
4
y
5
Assignment
• Section 7.3
• Page 453
• Problems #4-24 even