CHAPTER 8 RIGHT TRIANGLES 8.3 THE CONVERSE OF THE PYTHAGOREAN THEOREM

THE PYTHAGOREAN THEOREM Recall that the Pythagorean Theorem applies to all right triangles and shows that: a² + b² = c² or leg² + leg² = hypotenuse²

THEOREM 8-3 THEOREM 8-3 If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. Theorem 8-3 is the converse of the Pythagorean Theorem and says that if the Pythagorean Theorem works for a triangle, then it is right.

EXAMPLES Tell whether a triangle with given sides lengths is right 20, 21, 29 9, 15, 15 7, 24, 25 20, 21, 30 10, 24, 26 Yes No

If a² + b² = c², then ∆ABC is right. THEOREM 8-3 If a² + b² = c², then ∆ABC is right. B b a A C c

If a² + b² > c², then ∆ABC is acute. THEOREM 8-4 B If a² + b² > c², then ∆ABC is acute. b a A C c

If a² + b² < c², then ∆ABC is obtuse. THEOREM 8-5 B If a² + b² < c², then ∆ABC is obtuse. b a A C c

EXAMPLES Tell whether a triangle with the given side lengths is right, acute, or obtuse. 20, 21, 30 20, 21, 28 5, 6, 8 8, 15, 17 Obtuse Acute Right

CLASSWORK/HOMEWORK 8.3 Assignment Pg. 296, Classroom Exercises 1-10 all Pg. 297, Written Exercises 1-8, 11-14