The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It is represented by the formula a2 + b2 = c2, where a and b are the lengths of the two legs and c is the length of the hypotenuse. Several examples are given demonstrating how to use the theorem to solve problems involving right triangles, such as calculating the length of the hypotenuse, the length of one leg, or the distance across a soccer field.

1. Pythagorean Theorem
This is a __________
triangle.
Point to the hypotenuse of each
of these triangles.
Pythagorean Theorem:
The hypotenuse is always
a=
a2 + b2 = c2
b=
+
2 2
= 2
c=
+ =
=
=

2. 6
a2 + b2 = c2
+
2 2
= 2
x
+ =
=
3
=
a2 + b2 = c2
+
2 2
= 2
9 + =
=
x
=
4 a2 + b2 = c2
+
2 2
= 2
x
+ =
=
2
=
7
a2 + b2 = c2
x +
2 2
= 2
+ =
5 =
5 =

3. a2 + b2 = c2
The bottom of a ladder must be
placed 3 feet from a wall. The
ladder is 12 feet long. How far
2
+ 2
= 2
above the ground does the 12
ladder touch the wall?
x + =
=
=
3
a2 + b2 = c2
12 90
A soccer field is a rectangle 90
x 2
+ 2
= 2
0
meters wide and 120 meters 120
long. The coach asks players to 144 + 810 = X2
run from one corner to the 00 0
corner diagonally across. What
is this distance?
225 = X2
00
90
150= x
a2 + b2 = c2
15 12 X 15
How far from the base of the +
2 2
= 2
house do you need to place a 12
15-foot ladder so that it exactly
reaches the top of a 12-foot
144 + X2 = 225
tall wall?
X = 81
X
= 9
What is the length of the
a2 + b2 = c2
diagonal of a 10 cm by 15 cm
rectangle? 15 15
+
2 10 2
= X 2
X
225 + 100 = X2
325 =
10
= 18.
02
Click here to enter Summary

4. Go to the following link, and work until you have completed 10 problems correctly.
http://www.shodor.org/interactivate/activities/PythagoreanExplorer/