a

b

c

222 cba

Use the Pythagorean Theorem and its converse to solve problems.

Objectives

Pythagoras was a Greek philosopher and religious leader.He was responsible for many important developments in math,

astronomy, and

music.

Pythagoras (~560-480 B.C.)

His students formed a secret society called the Pythagoreans.

As well as studying maths, they were a political and religious organisation.

Members could be identified by a five pointed star they wore on their clothes.

The Secret Brotherhood

They had to follow some unusual rules. They were not allowed to wear wool, drink wine or pick up anything they had dropped! Eating beans was also strictly forbidden!

The Secret Brotherhood

Pythagoras realized that if you have a right triangle,

3

4

5

and you square the lengths of the two smaller sides,

24233

4

5

and add them together,

3

4

5

2423 22 43

22 43

you get the same number you would get by squaring the larger side.

222 543 3

4

5

Is that correct?

222 543 ?

25169 ?

It is, and it is true for any right triangle.

8

6

10222 1086

1006436

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

a

b

is called the

And the length of the hypotenuse

is usually labeled c.

a

b

c

The relationship Pythagoras discovered is now called The Pythagorean Theorem:

a

b

c

The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,

a

b

c

then

a

b

c

.222 cba

The Pythagorean Theorem is probably the most famous relationship in mathematics.

a2 + b2 = c2

Let’s practice !!!

Using the Pythagorean Theorem

Find the value of x. Give your answer in simplest radical form.

a2 + b2 = c2 Pythagorean Theorem

22 + 62 = x2 Substitute 2 for a, 6 for b, and x for c.

40 = x2 Simplify.

Find the positive square root.

Simplify the radical.

Check It Out! Example 1a

Find the value of x. Give your answer in simplest radical form.

a2 + b2 = c2 Pythagorean Theorem

42 + 82 = x2 Substitute 4 for a, 8 for b, and x for c.

80 = x2 Simplify.

Find the positive square root.

Simplify the radical.