#### Transcript of geomtery 8.1 The Pythagorean Theorem

**Finally**

**Pythagorean Theorem**

**8.1 The Pythagorean Theorem and its converse**

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Pythagorean Triple

Pythagorean Triple is a set of nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem equation.

If you were on the beach on the southeast corner of a lake and wanted to go across to reach the northwest corner of a lake how far would you have to travel by boat if the northwest beach was 176 meters west and 330 meters north of the southeast beach.

**Find the length of the missing side**

Converse of the Pythagorean theorem

If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

What do you notice if you square the length of the sides of each triangle?

(leg)

(leg)

(Hypotenuse)

1.) 3, 4, 5

2.) 5, 12, 13

3.) 8, 15, 17

4.) 7, 24, 25

5.) 9, 40, 41

Common Pythagorean Triple's

1.)

8

15

17

Is this a Pythagorean triple?

If you multiply each number in a Pythagorean Triple by the same whole number, the 3 numbers that result also form a Pythagorean triple.

12

16

20

3(4), 4(4), 5(4)

24

10

X

41

9

X

Solve for X.

Find the value of x. Make sure to leave your answer in simplest radical form and not decimal.

20

8

______

______

______

If

the triangle is

acute

If

the triangle is

obtuse

Is it a right triangle if the sides of a triangle are 8, 10, 12?

Classify the triangle whose side lengths are 15, 7, 11.

Pythagorean Theorem

where

C

is the

hypotenuse

where

C

is the

hypotenuse

X

1.

2.

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