Question

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.
Gina and Sean wrote the following proofs.

Gina’s Proof:

Step 1: Area of PQRS = (a + b) 2 = a2 + b2 + 2ab
Step 2: Area of triangle PKN =a multiplied by b, the whole multiplied by one-half.; hence the area of 4 triangles = 4 multiplied by the product of a and b, the whole multiplied by one-half is equal to twice the product of a and b.
Step 3: Area of KLMN = c2 = area of PQRS – area of 4 triangles = a2 + b2 + 2ab – 2ab
Hence, c2 = a2 + b2

Sean’s Proof:
Step 1: Area of triangle EAF =a multiplied by b, the whole multiplied by one-half.; hence the area of 4 triangles = 4 multiplied by the product of a and b, the whole multiplied by one-half is equal to twice the product of a and b.
Step 2: Area of square ABCD = (a – b) 2 = a2 + b2 – 2ab
Step 3: Area of EFGH = c2 = Area of 4 triangles + area of ABCD = 2ab + a2 + b2 – 2ab
Hence, c2 = a2 + b2

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

Both the proofs are correct.

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

Both the proofs are incorrect.

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

Answer 1

@FriedRice @Jamierox4ev3r @ziko1995

Answer 2

@Jamierox4ev3r can you help?

Answer 3

Both the proofs are correct :)

Answer 4

?

Answer 5

Oh, okay.

Answer 6

Thanks(:

Answer 7

Have a good day :)