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The Pythagorean Theorem • Pythagoras was one of the first mathematicians to recognize the relationship between the sides of a right triangle. This special relationship forms the Pythagorean Theorem. • The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. • According to the Pythagorean Theorem, the sum of the two green squares, is equal to the area of the blue square. Therefore in algebraic terms, the Pythagorean Theorem is stated as: Find the length of the hypotenuse ( ). Using the Pythagorean Theorem A right triangle is a triangle with an angle of 90º. T he two sides that form the right angle are called legs. The side opposite the right angle is the hypotenuse. Square A a hypotenuse • Area of square A = a2 • Area of square B = b2 • Area of square C = c2 right angle leg leg a2 + b2 = c2 a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 25 = c2 5 = C Square B Square C b c C C 3cm 4cm Substitute for the known variables. Take the square root of both sides. The length of the hypotenuse is 5cm. Pythagoras was a Greek mathematician and philosopher who made important contributions to mathematics and astronomy. The Pythagorean Theorem was Pythagoras’ most famous mathematical contribution. © Copyright NewPath Learning. All Rights Reserved. 93-4708 www.newpathlearning.com The Pythagorean Theorem

\|xiBAHBDy01689sz\ The Pythagorean Theorem • Area of square A = a2 • Area of square B = b2 • Area of square C = c2 • was one of the first mathematicians to recognize the relationship between the sides of a right triangle. This special relationship forms the . • The Pythagorean Theorem states • According to the Pythagorean Theorem, the sum of the two green squares, is equal to the area of the blue square. Therefore in algebraic terms, the Pythagorean Theorem is stated as: Find the length of the hypotenuse ( ). Using the Pythagorean Theorem A right triangle is a triangle with an of . The two sides that form the right angle are called . The side opposite the right angle is the . a2 + b2 = c2 a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 25 = c2 5 = C Square A a Square B Square C b c C C 3cm 4cm Substitute for the known variables. Take the square root of both sides. The length of the hypotenuse is 5cm . Key Vocabulary Terms • angle • hypotenuse • leg • Pythagorean Theorem • right triangle • side Pythagoras was a Greek mathematician and philosopher who made important contributions to mathematics and astronomy. The Pythagorean Theorem was Pythagoras’ most famous mathematical contribution. . © Copyright NewPath Learning. All Rights Reserved. 93-4708 www.newpathlearning.com The Pythagorean Theorem