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.


http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1008_07/image0034e8ca1c0.jpg
Hazel wrote the following statements to prove that c2 = x2 + y2.

Answer 1

1. Area of the four grey triangles inside figure A = http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/1008/1008_G7_Q26a.gif
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 = http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/1008/1008_G7_Q26b.gif
5. Area of the two white squares inside figure B = 2x2+ 2y2
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?

Answer 2

5
it's x2 + y2 i blive

Answer 3

its statement 8:
in A:
4grey = 2xy
2white = c^2
therefore A = 2xy + c^2

in B:
2white: = 2x^2+2y^2
and area B = 2x^2+2y^2+2xy
and if A=B, then
2xy + c^2 = 2x^2+2y^2+2xy
c^2= 2x^2+2y^2, therefore statement 8 is wrong.

Answer 4

These are my choices:
Statement 5

Statement 6

Statement 7

Statement 4

Answer 5

I thought it was statement 8 too but apparently its not

Answer 6

let me see, just a minute:

Answer 7

I get it since 1 and 4 are the same, then by same thinking then statement 5 should equal twice statement 2, hence 5 should read 2c^2 instead of 2x2+ 2y2, and hence 5 must be incorrect, what do you think?

Answer 8

sounds good