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The Converse of the Pythagorean Theorem . Observe the relationship between the measure of C and the squares of the lengths of the sides of ∆ ABC in the Sketchpad diagram In what type of triangle is c 2 = a 2 + b 2 In what type of triangle is c 2 < a 2 + b 2
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The Converse of the Pythagorean Theorem • Observe the relationship between the measure of C and the squares of the lengths of the sides of ∆ABC in the Sketchpad diagram • In what type of triangle is c2 = a2 + b2 • In what type of triangle is c2 < a2 + b2 • In what type of triangle is c2 > a2 + b2 B c a C A b
The Converse of the Pythagorean Theorem Converse of the Pythagorean Theorem • If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle • If the lengths of the three sides of a triangle satisfy the Pythagorean theorem, then the triangle is a right triangle • Classifying a triangle by the lengths of its sides • If c2 = a2 + b2 then ∆ABC is a right triangle • If c2 < a2 + b2 then ∆ABC is an acute triangle • If c2 > a2 + b2 then ∆ABC is an obtuse triangle B c a C A b
