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aselhajj1 Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music.

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aselhajj2 In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse... a 2 + b 2 = c 2 The hypotenuse is the side that faces the right angle and its always the longest hypotenuse (c) leg (a) leg (b) The Pythagorean Theorem

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aselhajj3 What is the length of the hypotenuse ? Step 1. Write the formula for the Pythagorean Theorem. Step 2. Substitute in known values. Step 3. Solve for the unknown variable. a 2 + b 2 = c 2 8 2 + 15 2 = c 2 64 + 225 = c 2 289 = c 2 The Pythagorean Theorem

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aselhajj4 A television screen measures approximately 15.5 in. high and 19.5 in. wide. A television is advertised by giving the approximate length of the diagonal of its screen. How should this television be advertised? Draw and label a diagram to model the problem. 15.5 19.5 c Solve for c, using the Pythagorean Theorem. The television should be advertised as a 25.

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aselhajj5 Ladder Problem A ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window?

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aselhajj6 Distance from house: 7 meters First draw a diagram that shows the right triangle. Label the sides: –Ladder is 25 m –Distance from house is 7 m Use Pythagorean theorem a 2 + b 2 = c 2 to solve Ladder Problem 7 2 + b 2 = 25 2 49 + b 2 = 625 b 2 = 576 b = 24

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aselhajj7 A set of three whole numbers a, b, and c such that a 2 + b 2 = c 2 is called a Pythagorean triple. Pythagorean Triples

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aselhajj8 Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. Since the side lengths are whole numbers that satisfy the equation a 2 + b 2 = c 2, so they form a Pythagorean triple. a 2 + b 2 = c 2 14 2 + 48 2 = c 2 2500 = c 2 50 = c 14 48

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aselhajj9 Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a 2 + b 2 = c 2 8 2 + 10 2 = c 2 164 = c 2 The side lengths do not form a Pythagorean triple because is not a whole number. 8 10

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aselhajj10 You can also use Pythagorean theorem to classify a triangle as acute or obtuse. Pythagorean Inequalities: c2 < a2 + b2 - - - Triangle is acute c 2 > a 2 + b 2 - - - Triangle is obtuse c2 = a2 + b2 - - - Triangle is Right

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aselhajj11 Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 7, 10 Since c 2 > a 2 + b 2, the triangle is obtuse. 100 > 74 c 2 = a 2 + b 2 ? 10 2 = 5 2 + 7 2 ? 100 = 25 + 49 ?

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aselhajj12 7, 12, 16 Since c 2 > a 2 + b 2, the triangle is obtuse. 256 > 193 c 2 = a 2 + b 2 ? 16 2 = 12 2 + 7 2 ? 256 = 144 + 49 ?

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KS4 Mathematics S2 Pythagoras’ Theorem.

KS4 Mathematics S2 Pythagoras’ Theorem.

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