# 8.1 Pythagorean Theorem and Its Converse

## Presentation on theme: "8.1 Pythagorean Theorem and Its Converse"— Presentation transcript:

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.

Finding the Length of the Hypotenuse
What is the length of the hypotenuse in Triangle ABC?

Finding the Length of the Leg

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 + b² 14² ___ 6² + 11² 196 ___ 196 > 157 The triangle is obtuse.

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