Transcript Proportions in Right Triangles

Proportions in Right Triangles
Theorem 7.1
• The altitude to the
hypotenuse of a
right triangle forms
two triangles
similar to it and
each other.
ABC~ADB ~ BDC
B
C
A
D
Proportions in Right Triangles
Geometric mean – For
two positive numbers
a and b, the geometric
mean is the positive
number x where the
proportion a/x = x/b is
true. In other words, x
= ab.
B
C
A
D
a. Find the geometric mean between 3 and 12.
Answer: 6
b. Find the geometric mean between 4 and 20.
Answer: 8.9
Proportions in Right Triangles
Theorem 7.2
• The altitude to the hypotenuse
of a right triangle is the
geometric mean between the
segments into which it divides
the hypotenuse.
B
AD:BD = BD:CD
Theorem 7.3
• Each leg of a right triangle is
the geometric mean between
the hypotenuse and its
projection on the hypotenuse.
AC:AB = AB:AD
AC:BC = BC:DC
C
A
D
Answer: about 8.5
Find e and f.
f
Answer:
AIRPLANES A jetliner has a wingspan, BD, of 211
feet. The segment drawn from the front of the plane to
the tail,
intersects
at point E. If AE is 163 feet,
what is the length of the aircraft?
Answer: about 231.3 ft