Question

Explain? :l

Gina and Sean drew the following figures to prove the Pythagorean Theorem c2 = a2 + b2. Both figures are made of two squares and four identical right triangles, as shown below.\

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1000_Subtest_02_05/image0054e8c5217.jpg



Gina and Sean wrote the following proofs.

Gina’s Proof: Step 1: Area of PQRS = (a + b)^2=a^2+b^2+ 4ab.
Step 2: Area of triangle PKN=1/2ab; hence the area of 4 triangles = 4ab.
Step 3: Area of KLMN=c^2=area of PQRS – area of 4 triangles=a^2+b^2+ 4ab – 4ab.

Answer 1

Hence, c^2=a^2+b^2.
Sean's proof:
Step 1: Area of triangle EAF =1/2ab ; hence the area of 4 triangles = 4[1/2 ab]=2ab
Step 2: Area of square ABCD = (a – b)^2 = a^2 + b^2 – 2ab
Step 3: Area of EFGH = c^2 = Area of 4 triangles + area of ABCD = 2ab + a^2 + b^2 – 2ab
Hence c^2 = a^2 + b^2

Answer 2

Which statement gives the correct conclusion about the proofs given by Gina and Sean?

Sean’s proof is correct and Gina’s proof is incorrect.

Both the proofs are correct.

Gina’s proof is correct and Sean’s proof is incorrect.

Both the proofs are incorrect.

Answer 3

http://assets.openstudy.com/updates/attachments/4fac40e0e4b059b524f7ffd1-poptartninjaxp-1336688925399-proofs.png

Answer 4

both the proofs are correct

Answer 5

Thanks(:

Answer 6

:)