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**8.1 Pythagorean Theorem and Its Converse**

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.

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**Finding the Length of the Hypotenuse**

What is the length of the hypotenuse in Triangle ABC?

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Simplest Radical Form Simplify

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Simplest Radical Form Simplify

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**Finding the Length of the Leg**

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

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**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.

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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.

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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)

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**Classifying a Triangle**

A triangle has side lengths 6, 11, and 14. Is it acute, obtuse, or right? c² ___ a² + b² 14² ___ 6² + 11² 196 ___ 196 > 157 The triangle is obtuse.

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More Practice!!!!! Homework – Textbook p. 495 – 496 #8 – 32 EVEN.

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