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.

1. Area of the four grey triangles inside figure A = 4(1/2xy) = 2xy
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 figu

Answer 1

B = x2+ y2 + 4xy
7. Area of figure A = area of Figure B, hence c2 + 2xy = x2+ y2 + 4xy
8. Therefore, c2 = x2+ y2

Which is the first incorrect statement in Hazel’s proof?
Answer

Statement 4

Statement 5

Statement 6

Statement 7

Answer 2

How the statement 2 is correct? It is a rhombus. Angles are not 90 degree.

Answer 3

Once 2 is false, 3 is also false.

Answer 4

so just say 4 is the first one wrong?

Answer 5

Yes, that (4) is also wrong.

Answer 6

ok thank you