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

Some common Pythagorean Triples are: 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? 20 8 x 20 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.

Applying the Converse of the Pythagorean Theorem If , complete each statement. Are the following triangles right triangles? EXPLAIN 85 84 13 21 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 B c a A C b

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 B c a A C b

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?