Question

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.
Hazel wrote the following statements to prove that c2 = x2 + y2.

Answer 1

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 = 4xy
5. Area of the two white squares inside figure B = x2+ y2
6. Area of figure B = x2+ y2 + 4xy
7. Area of figure A = area of Figure B, hence c2 + 2xy = x2+ y2 + 4xy
8. Therefore, c2 = x2+ y2