Transcript Document

a b c
2
c
a
b
2
2
This is a right triangle:
We call it a right triangle
because it contains a
right angle.
The measure of a right
o
angle is 90
90o
The little square in the
angle tells you it is a
right angle.
90o
About 2,500 years ago, a
Greek mathematician named
Pythagorus discovered a
special relationship between
the sides of right triangles.
Pythagorus realized that if
you have a right triangle,
5
3
4
and you square the lengths
of the two sides that make
up the right angle,
5
3
2
4
3
4
2
and add them together,
5
3
3 4
2
4
2
you get the same number
you would get by squaring
the other side.
5
3
3 4 5
2
4
2
2
Is that correct?
2 ?
3 4 5
2
?
2
9  16  25
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 two sides which
come together in a right
angle are called
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
Suppose
can use
youThe
drive
Pythagorean
directly
Theorem
west for 48
to miles,
solve many kinds
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
Why?
Can
you see that we have a
right triangle?
2
2
48 + 36 = c
2
36
48
c
Which sides
side isare
thethe
hypotenuse?
legs?
2
2
48 + 36 = c
2
36
48
c
Then all we need to do is
calculate:
48  36  2304 1296 
2
2
3600  c
2
2
Andsince
So,
you end
c isup
3600,
60 miles
c is 60.
from
where you started.
48
36
60
Find the length of a diagonal
of the rectangle:
15"
?
8"
Find the length of a diagonal
of the rectangle:
15"
b=8
c
?
a = 15
8"
15
225
a
cc 
17
864
b289 c
2
b=8
c
a = 15
2
2
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