anonymous
  • anonymous
The figures below show two different ways of arranging four identical triangles of grey poster board on top of a white square. The square has sides equal to x + y, while the hypotenuse of each triangle is represented by the variable c.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
Hazel wrote the following statements to prove that c2 = x2 + y2. 1. Area of the four grey triangles inside figure A = A equals four times the quantity one-half times x times y, which equals 2 times x times y. 2. Area of the white square inside figure A = c2 3. Area of figure A = c2 + 2xy 4. Area of the four grey triangles inside figure B = A equals four times the quantity one-half times x times y, which equals 2 times x times y. 5. Area of the two white squares inside figure B = x2+ y2 6. Area of figure B = 2x2+ 2y2 + 2xy 7. Area of figure A = area of Figure B, hence c2 + 2xy = 2x2+ 2y2 + 2xy 8. Therefore, c2 = x2+ y2 Which is the first incorrect statement in Hazel’s proof? Statement 7 Statement 4 Statement 5 Statement 6

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