Why don't you sleep with the pigs, cindersoot, if you insist on smelling like one.

8.1 The Pythagorean Theorem

& Its Converse

Pythagorean Theorem

Theorem 8-1: Pythagorean Theorem – 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.

a2+b2=c2

a

bc

**Warning- c is ALWAYS the hypotenuse while a and b are the other two legs of the triangle

Pythagorean Theorem

Pythagorean Triple: A set of nonzero whole numbers, a, b, and, c

that makes a2+b2=c2 a true statement.

Some common Pythagorean Triples are:

3, 4, 5

5, 12, 13

8, 15, 17

7,24,25

Applying the Pythagorean Theorem

Find the value of the missing length. Do the lengths of sides of

ABC form a Pythagorean Triple?

208

x20

21

x

Converse of the Pythagorean Theorem

Theorem 8-2: Converse of the Pythagorean Theorem – If the square of the lengths 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.

If a2+b2=c2, then the triangle is a right triangle.

If , complete each statement.

Applying the Converse of the Pythagorean Theorem

Are the following triangles right triangles? EXPLAIN

8584

1321

20

28

Classifying Triangles

Theorem 8-3: If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse.

If c2 > a2+b2, then the triangle is obtuse

A

B

C

a

b

c

Classifying Triangles

Theorem 8-4: If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is acute.

If c2 < a2+b2, then the triangle is acute

A

B

C

a

b

c

Classifying Triangles

Classify the triangles as Acute, Obtuse, or Right

Given a triangle with sides 6, 11, and 14 how can you classify the triangle?

Given a triangle with sides 7, 8, and 9 how can you classify the triangle?

Application

The Parks Department rents paddle boats at docks near each entrance to the park. To the nearest meter how far is it to paddle from one dock to the other?

My 9th grade science teacher always said that if you put a frog in boiling hot water, it would jump out, but put it in cold water, and heat it up gradually, it would slowly boil to death. What is it to you?

8.1 The Pythagorean Theorem and its Converse

Section 8.1; Pg. 420; 2-28 evens , 36, 38, 49