a b c
2
c
a
b
2
2
The measure of a right
o
angle is 90
90o
Pythagorus realized that if
you have a right triangle,
5
3
4
It is. And it is true for any
right triangle.
6  8  10
2
2
2
10
8
36  64  100
6
The two sides which
come together in a right
angle are called
The lengths of the legs are
usually called a and b.
a
b
The side across from the
right angle is called the
a
b
And the length of the
hypotenuse
is usually labeled c.
a
c
b
The relationship Pythagorus
discovered is now called
The Pythagorean Theorem:
a
c
b
The Pythagorean Theorem
says, given the right triangle
with legs a and b and
hypotenuse c,
a
c
b
then a  b  c .
2
a
2
c
b
2
You
can use
Pythagorean
Suppose
youThe
drive
directly
Theorem
to miles,
solve many kinds
west for 48
of problems.
48
Then turn south and drive for
36 miles.
48
36
How far are you from where
you started?
48
36
?
Using The Pythagorean
Theorem,
2
2
48 + 36 = c
2
36
48
c
Find the length of a diagonal
of the rectangle:
15"
?
8"
Find the length of a diagonal
of the rectangle:
15"
17
8"
Practice using
The Pythagorean Theorem
to solve these right triangles:
c = 13
5
12
b
10
26
b = 24
a b c
2
2
2
10  b  26
2
100  b  676
2
b  676  100
2
b  576
2
2
2
10 (a)
26
(c)
b  24
12
b= 9
15