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The Pythagorean Theorem

The Right Triangle

A right triangle is a triangle

that contains one right

angle.

A right angle is 90o

Right Angle

Parts of a Right Triangle

Leg

Hypotenuse

Leg

The Pythagorean Theorem

a2 + b2 = c2

c

a

b

Example 1

Find the length of the hypotenuse.

c

4

3

Example 2

Find the length of the hypotenuse.

c

8

6

Example 3

Find the length of the hypotenuse

c

16

12

Example 4

Find the length of the unknown side

b

13

12

Example 5

Find the length of the unknown side.

17

15

a

Example 7

Find the length of the unknown side.

24

b

25

Pythagorean Triple

All of the side lengths of the triangles we

have looked at form Pythagorean Triples.

If the side lengths of a right triangle are all

whole numbers, they are called

Pythagorean Triples.

Pythagorean Triples

List the Pythagorean Triples we have

discussed.