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Pythagoras (580 - 500 B.C.)

Pythagoras (580 - 500 B.C.) He was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music. hypotenuse (c). leg (b). leg (a). The Pythagorean Theorem.

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Pythagoras (580 - 500 B.C.)

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

  2. hypotenuse(c) leg(b) leg(a) The Pythagorean Theorem 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. . . a2+b2= c2 The hypotenuse is the side that faces the right angle and it’s always the longest aselhajj

  3. The Pythagorean Theorem What is the length of the hypotenuse ? Step 1. Write the formula for the Pythagorean Theorem. a2+b2= c2 Step 2. Substitute in known values. 82+152= c2 Step 3. Solve for the unknown variable. 64+225= c2 289= c2 aselhajj

  4. c 15.5 19.5 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. Solve for c, using the Pythagorean Theorem. The television should be advertised as a 25”. aselhajj

  5. 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? aselhajj

  6. Ladder Problem 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 theorema2 + b2 = c2to solve 72+b2= 252 49+b2= 625 b2= 576 b= 24 aselhajj

  7. Pythagorean Triples A set of three whole numbers a, b, and c such that a2 + b2 = c2 is called a Pythagorean triple. aselhajj

  8. 14 48 Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a2 + b2 = c2 142 + 482 = c2 2500 = c2 50 = c Since the side lengths are whole numbers that satisfy the equation a2 + b2 = c2, so they form a Pythagorean triple. aselhajj

  9. 8 10 Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a2 + b2 = c2 82 + 102 = c2 164 = c2 The side lengths do not form a Pythagorean triple because is not a whole number. aselhajj

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

  11. ? c2 = a2 + b2 ? 102 = 52 + 72 ? 100 = 25 + 49 Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 7, 10 100 > 74 Since c2 > a2 + b2, the triangle is obtuse. aselhajj

  12. ? c2 = a2 + b2 ? 162 = 122 + 72 ? 256 = 144 + 49 7, 12, 16 256 > 193 Since c2 > a2 + b2, the triangle is obtuse. aselhajj

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