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7.1-2 The Pythagorean Theorem Mrs. Wilkins Geometry Objectives/Assignment •Prove the Pythagorean Theorem •Use the Pythagorean Theorem to solve real-life problems such as determining how far a ladder will reach. History Lesson •Around the __ century BC, the Greek mathematician Pythagorus founded a school for the study of _____, mathematics and science. Many people believe that an early ___ of the Pythagorean Theorem came from this school. •Today, the ___________ is one of the most famous theorems in geometry. Over ___ different proofs now exist. Theorem 9.4: Pythagorean Theorem •In a _____ triangle, the square of the length of the hypotenuse is equal to the ___ of the squares of the legs. c a b a2 + b2 = c2 Ex. 1: Finding the length of the hypotenuse. •Find the value of x. 12 5 x Ex. 2: Finding the length of the leg. •Find the value of x. 15 x 26 Ex. 3: Finding the length of the leg. •Find the value of x. Ex. 4 Finding the length of the hypotenuse. •Find the value of x. x 19 8 Is the triangle acute, obtuse or right? RIGHT ACUTE OBTUSE Ex. 5 Classify the triangles given their side lengths • 10, 11, 14 • 6, 8, 10 • 12, 16, 20 • 4, 7, 9 • 5, 6, 7 • 15, 36, 39 7.1-2 The Pythagorean Theorem Mrs. Wilkins Geometry Find the unknown side length x 18 12 Find the unknown side length x 4 √5 Find the unknown side length x x 2√5 Find the unknown side length 20 12 x Using the Pythagorean Theorem •A Pythagorean triple is a set of _____ positive integers a, b, and c that satisfy the equation _________. For example, the integers 3, 4 and 5 form a Pythagorean Triple because 32 + 42= 52. Pythagorean Triples 3,4, 5 5, 12, 13 8, 15, 17 7, 24, 25 The given lengths are two sides of a right triangle. The sides together form a Pythagorean triple. Find the length of the third side and tell whether it is a leg or the hypotenuse. •24 and 51 •20 and 25 •72 and 75 Pythagorean Triples 3,4, 5 5, 12, 13 6, 8, 10 15, 36, 39 8, 15, 17 7, 24, 25 Classify the triangles given their side lengths 14, 25, 30 55, 7, 10 31,15, 16