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## Lesson 6-6

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**Lesson 6-6**The Pythagorean Theorem**Ohio Content Standards:**Find the square root of perfect squares, and approximate the square root of non-perfect squares.**Ohio Content Standards:**Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., (square root of 130) is between 11 and 12.**Ohio Content Standards:**Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.**Ohio Content Standards:**Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals.**Ohio Content Standards:**Estimate the solutions for problem situations involving square and cube roots.**Ohio Content Standards:**Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.**Ohio Content Standards:**Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:a. prove the Pythagorean Theorem;b. prove theorems involving triangle similarity and congruence;c. prove theorems involving properties of lines, angles, triangles and quadrilaterals;d. test a conjecture using basic constructions made with a compass and straightedge or technology.**Ohio Content Standards:**Use right triangle trigonometric relationships to determine lengths and angle measures.**Ohio Content Standards:**Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures.**Pythagorean Theorem**In a right triangle, the square of the lengths of the hypotenuse c is equal to the sum of the squares of the lengths of the legs a and b.**Pythagorean Theorem**In a right triangle, the square of the lengths of the hypotenuse c is equal to the sum of the squares of the lengths of the legs a and b. a2+ b2 = c2**Pythagorean Theorem**c a b a2 + b2 = c2**Find the length of the hypotenuse of the right triangle.**16 ft 12 ft**Find the length of one leg of a right triangle if the length**of the hypotenuse is 4 meters and the length of the other leg is 3 meters. 4 m 3 m**If c is the measure of the hypotenuse, find the missing**measure. Round to the nearest tenth, if necessary. a = ?, b = 10, c = 20**The lengths of the three sides of a triangle are 4, 5, and 6**meters. Determine whether this triangle is a right triangle.