### The Pythagorean Theorem

```The Pythagorean Theorem
Objectives
• The objective of this lesson is for you to learn
and apply the Pythagorean Theorem -- an
important relationship between the three
sides of a right triangle.
The Theorem
• One of the most important and fundamental
theorems in all of mathematics
• Where a and b are the two legs of the right
triangle and c is the hypotenuse.
Sample Problem
• If the two legs of a right triangle measure 3
and 6, then what is the length of the
hypotenuse?
Basic Problems
• If the two legs of a right triangle measure 5
and 12, then what is the length of the
hypotenuse?
• If the hypotenuse of a right triangle measures
10 and one leg measures 5, then what is the
length of the other leg?
Problems
• Find out the length of sides a and b on the
following triangle:
Problems
• What is the longest straight pole, like the red
one, that you can have inside the box?
Application Problems
• There is a building with a 12 ft high window.
You want to use a ladder to go up to the
window, and you decide to keep the ladder 5
ft away from the building to have a good slant.
How long should the ladder be?
• On a baseball diamond the bases are 90 ft
apart. What is the distance from home plate
to second base in a straight line?
Pythagorean Triples
• Pythagorean Triples are sets of three integer
values that satisfy the Pythagorean Theorem
• Common Triples
( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17)
( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)
(16,63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65)
(36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)
```