Introduction to Chapter 4: Pythagorean Theorem and Its Converse

Introduction to Chapter 4: 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 2 2 a b c 20 21 c 2 2 400 441 c 841 c 2 2 841 c 2 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 a b c 2 2 2 8 x 20 2 2 64 x 400 2 x 336 2 x 336 x 16(21) x 4 21

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.

Obtuse and Acute Triangles 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 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 36 121 196 157 The triangle is obtuse.

Homework Worksheet: The Pythagorean Theorem and Its Converse #’s 1-18