**The Pythagorean theorem**

For right triangles

a + b = c

Where a, b and c are legs and c is the hypotenuse.

We will use the Pythagorean theorem to find missing side lengths

If the missing side is a leg

If the missing side is the hypotenuse

2

2

2

Step 1 -

Step 2 -

Step 3 -

Step 4 -

Identify a, b and c

Plug a, b and c into Pythagorean Theorem

Simplify equation

Solve for missing value

1.

Label a, b, c

Write Pythagorean theorem

Substitute a, b and c

Simplify exponents

Add !

Take square root of both sides

Simplify if needed

2.

3.

4.

5.

6.

7.

Label a, b, c

Write Pythagorean theorem

Substitute a, b and c

Simplify exponents

Take square root of both sides

Simplify if needed

Subtract !

1.

2.

3.

4.

5.

6.

7.

18

15

10

8

In a right triangle, the sum of the squares of the legs has a special relationship with the square of the hypotenuse. What is this relationship?

**Investigation**

**A long time ago in a land**

far far away...

far far away...

Your best guess about a

mathematical relationship.

It is usually a generalization about a

pattern

you think might be true, but that you do not yet know for sure is true.

**Conjecture**

The sum of the square of the legs of a right triangle

equals

the square of the hypotenuse.

**Let's get Conjectural**

a

b

c

**a**

**b**

**c**

**=**

**+**

2

2

2

Where is the

Hippos home?

label the hypotenuse with the letter c

How can we correct the Scarecrow’s statement so it is mathematically precise?

**Can you correct the Scarecrow?**