8.1 Pythagorean Theorem and Its Converse

• Pythagorean Theorem– If a triangle is a right triangle, then the sum of the

squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Finding the Length of the Hypotenuse

• What is the length of the hypotenuse in Triangle ABC?

2 2 2a b c 2 2 220 21 c

2400 441 c 2841 c2841 c 29 c

Simplest Radical Form

• Simplify 20.

20 4 5

4 5

2 5

Simplest Radical Form

• Simplify 192.

192 64 3

64 3

8 3

Finding the Length of the Leg

• What is the value of x? Express your answer in simplest radical form.

2 2 2a b c 2 2 28 20x

264 400x 2 336x 2 336x

16(21)x

4 21x

Converse of the Pythagorean Theorem• If the sum of the squares of the lengths of two sides of

a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

Theorems 8.3 and 8.4

• 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.

• 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.

Pythagorean Triples• A Pythagorean triple is a set of nonzero whole

numbers, a, b, and c that always satisfy the equation a² + b² = c².

• Some common Pythagorean Triples:3, 4, 5

5, 12, 13

8, 15, 17

7, 24, 25

• Keep an eye out for the multiples of these common Pythagorean Triples (ex. 6, 8, 10)

Classifying a Triangle

• A triangle has side lengths 6, 11, and 14. Is it acute, obtuse, or right?

c² ___ a² + b²14² ___ 6² + 11²196 ___ 36 + 121196 > 157

The triangle is obtuse.

More Practice!!!!!

• Homework – Textbook p. 495 – 496 #8 – 32 EVEN.