Transcript 7-1 and 7-2 Geometric Mean and Pygthagorean Thm

Geometric Mean &
the Pythagorean Thm.
Section 7-1 & 7-2
The geometric mean between 2
positive numbers a and b is the
positive number x where a
x
2
x =
ab
x = ab
x

b
Thm. 7-1
If the altitude is drawn from the
vertex of the right angle of a right
triangle to its hypotenuse, then the
2 triangles formed are similar to
the given triangle and to each
other.
C
A
D
B
ADC ~ CDB
Thm. 7-2
The measure of the altitude drawn
from the vertex of the right angle
of a right triangle to its hypotenuse
is the geometric mean between the
measures of the 2 segments of the
hypotenuse.
h
a
b
a h

h b
Thm. 7-3
If the altitude is drawn to the
hypotenuse of a right triangle, then
the measure of a leg of the triangle
is the geometric mean between the
measures of the hypotenuse and
the segment of the hypotenuse
adjacent to that leg.
a
h
d
c a

a d
b
e
c
c b

b e
Pythagorean Theorem
In a right triangle, the sum of the
squares of the measures of the legs
equals the square of the measure of
the hypotenuse.
c
2
2
2
a
a +b =c
b
Converse is also true.
Pythagorean Triples
If the measures of a right triangle
are whole numbers, the measures
of the sides are a Pythagorean
triple.
3-4-5
5-12-13
8-15-17
7-24-25
Joke Time
What is a twip?
A twip is what a wabbit takes
when he wides on a twain.
What is gray, has big ears
and has a trunk?
A mouse going on vacation