Transcription of CHAPTER 9 The Pythagorean Theorem
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CHAPTER 9 The Pythagorean Theorem
CHAPTER9 But serving up an action, suggestingthe dynamic in the static, has become ahobby of mine .. The flowing on thatmotionless plane holds my attention to such adegree that my preference is to try and make it into a C. ESCHERW aterfall,M. C. Escher, 1961 2002 Cordon Art B. V. Baarn rights PythagoreanTheoremOBJECTIVESIn this CHAPTER you will discover the PythagoreanTheorem, one of the mostimportant concepts inmathematics use the PythagoreanTheorem to calculate thedistance between any two points use conjectures related tothe Pythagorean Theoremto solve problemsCHAPTER 9 The Pythagorean Theorem461 Escher has cleverly used right angles to form hisartwork known as Wa t e r f a l l .The picture containsthree uses of the impossible tribar created byBritish mathematician Roger Penrose (b 1931) in1954.
measures 90° and the quadrilateral is a square. If it is a square with side length c, then its area is c2.So,a2 b2 c2, which proves the Pythagorean Theorem. ba b a a b b a c c c c The Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. Ifa and b are the ...
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