Question

Can you please help me with Geometry Proofs?

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.

Answer 1

Gina and Sean wrote the following proofs.

Gina’s Proof:

Step 1: Area of PQRS = (a + b) 2 = a2 + b2 + 4ab
Step 2: Area of 4 triangles = 4ab
Step 3: Area of KLMN = c2 = area of PQRS – area of 4 triangles = a2 + b2 + 4ab – 4ab
Hence, c2 = a2 + b2

Sean’s Proof:

Step 1: Area of triangle EAF = ab; hence the area of 4 triangles = 4ab
Step 2: Area of square ABCD = (a – b) 2 = a2 + b2 – 4ab
Step 3: Area of EFGH = c2 = Area of 4 triangles + area of ABCD = 4ab + a2 + b2 – 4ab
Hence c2 = a2 + b2

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

Both the proofs are incorrect.

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

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

Both the proofs are correct.