9.2 The Pythagorean Theorem

Did Pythagoras of Samos discover the Pythagorean

theorem?

The Pythagorean Theorem

In a Right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.

a

b

c

222 cba

The Pythagorean Theorem

In a Right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.

c

222 cba

7

24 25

247 22

c

c

Pythagorean Triples

If the sides of a Right triangle are integers, then the sides are known as a Pythagorean Triple

7, 24, 25

Do you know any other ?

Pythagorean Triples

If the sides of a Right triangle are integers, then the sides are known as a Pythagorean Triple

7, 24, 25

Do you know any other ?

3, 4, 5

5, 12, 13

Solve for x

A Right Triangle

x12

56

222

1256 x

Solve for x

A Right Triangle

x12

56

6

36

144180

144536

1256

2

2

2

222

x

x

x

x

x

Area and the Right Triangle

Area equals ½ altitude times base A=½ab

b and a are the same as the legs of a Right triangle.

3

4

6

432

1

A

A

2 poles are supported by 100ft cables 50 ft from the ground

How far are the poles apart?

ft100ft100 ft100

ft100

ft50 ft50

2 poles are supported by 100ft cables 50 ft from the ground

How far are the poles apart?

ft100ft100 ft100

ft100

ft50 ft50

x x

6.86350

7500

250010000

50100

2

2

222

x

x

x

x

2 poles are supported by 100ft cables 50 ft from the ground

How far are the poles apart?

ft100ft100 ft100

ft100

ft50 ft50

x x

ft2.1736.866.86

Solve for y

Use the Right Triangle

5y

1y

222 15 yy

Solve for y

Use the Right Triangle

5y

1y

13

226

0262

262

1225

15

22

22

222

y

y

y

yyy

yyy

yy

Homework

Page 538 – 541

# 8 – 24 even,

25 - 31, 33, 34,

39, 40

• The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they fitted it into a mathematical framework. http://en.wikipedia.org/wiki/Pythagorean_theorem#Proof_using_similar_triangles