1. Warm up 1. 3. 2.

2. Pythagorean Theorem Pythagoras was a Greek philosopher and teacher
He lived from 569 to 495 B. C.
Often described as the “first pure mathematician”

3. Pythagorean theorem – only “works” for right triangles
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
Hypotenuse (c) across from the “box”
Leg (b)
Leg (a)

4. Ex1: 10 6 x a b
Identify your hypotenuse ( c )
The other two sides are legs (it doesn’t matter which on you assign a or b
Plug into formula
Remember order of operations - SQUARE sides first and solve c
62 + x2 = 102
36 + x2 = 100
-36
x2 = 64
x = 8

5. Example
How high up a wall will a 20’ ladder touch if the ladder is placed 5’ from the wall?
Step 1:
Identify the hypotenuse and label it “c”
Wall
Ladder
20’
Step 2:
Label the other two sides as “a” and “b”
hypotenuse b c
Step 3:
Plug in and solve. 5’ a or

6. Ex3: y c a b
Follow the steps -5

7. Classwork Solve for the missing side.
Ex. 1
Ex. 2 5 x y
= 3 1
Ex. 3 4 2 6 z
= 5

8. Pythagorean Triples
Any three positive integers which fit the Pythagorean equation are called Pythagorean Triples.
Common Pythagorean Triples are…
3, 4, 5
5, 12, 13
7, 24, 25

9. Homework
Worksheet