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4.7 – Square Roots and The Pythagorean Theorem

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SQUARES and SQUARE ROOTS: Consider the area of a 3'x3' square: A = 3 x 3 A = (3) 2 = 9

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= 3 or what POSITIVE number you can multiply by itself to result in the answer of 9. 3 is called the SQUARE ROOT of 9 = 3

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Squares and Square Roots you should know: Estimate the square roots of the following numbers and then use your calculator to compute the actual values: 1) 2) 3) 4) x123456789101112131415 x2x2 149162536496481100121144169196225

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THE PYTHAGOREAN THEOREM: Pythagoras was a Greek mathematician from 6 th century BC. He discovered a unique relationship between the sides of a right triangle.

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The sides adjoining the right angle are called the LEGS of the triangle. The side opposite the right angle is called the HYPOTENUSE.

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Pythagorean Right Triangle Theorem: The sum of the squares of the legs of a right triangle is equal to the SQUARE of the hypotenuse. In symbols: if a and b are the legs and c is the hypotenuse of the right triangle then:

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Conversely: If the square of the length of one side of a triangle equals the SUM of the squares of the other two sides then the triangle is a RIGHT triangle.

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Examples: 1.) If the sides of a triangle measure 5, 12, and 13 inches can it be a right triangle? Pythagorean Formula: a 2 + b 2 = c 2 a = subs: + = b = results: + = c = = YES or NO

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Examples: 1.) Is the triangle that has sides that measure: 1, 1.5, and 2 yards a right triangle? Pythagorean Formula: a 2 + b 2 = c 2 a = subs: + = b = results: + = c = = YES or NO

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Homework : Section 4.7 pages 253-255 #’s 6-48 EVEN

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