Warm upMake a chart in your notes of the perfect squares from 1 to 20.

For Example:12 = 122 = 4

Pythagorean Theorem

Year 2Sections 9.1 and 9.2

Old Greek Guy

Pythagoras was a Greek philosopher and teacher

He lived from 569 to 495 B. C.

Often described as the “first pure mathematician”

The Theorem itself

For right triangles, where a and b are the legs and c is the hypotenuse of the triangle.

There are more than 200 known proofs. Check out a proof of the Theorem online at

http://www.keymath.com/x19481.xml

222 cba

2 2 25 20b

Example

How high up a wall will a 20’ ladder touch if the ladder is placed 5’ from the wall?

2 2 2a b c

5’

Ladder

20’ Wall

Step 1:

Identify the hypotenuse and label it “c”

hypotenusec

Step 2:

Label the other two sides as “a” and “b”

aStep 3:

Plug in and solve.

b2

2

25 400

375

5 15

b

b

b

19.4bor

Solve for the missing side.Ex. 1

Ex. 2

Ex. 3

5

x

4

1

2

y

61 6

z

= 3

= 5

5

Pythagorean Triples

Any three positive integers which fit the Pythagorean equation are called Pythagorean Triples.

Common Pythagorean Triples are…

3, 4, 55, 12, 13

7, 24, 25

Homework

Worksheet 9.1