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.

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.

Answer 2

tips?

Answer 3

could you guide me step by step with this problem?

Answer 4

both r incorrect right?

Answer 5

GINA proof, look at step one, the identity used is wrong

Answer 6

and SEAN proff,look at step 2, the identity used is again wrong

Answer 7

what do you mean?

Answer 8

the area of a square is l times w, right?

Answer 9

why is it quantity squared?

Answer 10

gina used (a+b)2=a2+b2+4ab but the correct identity is (a+b)2=a2+b2+2ab

Answer 11

and similarly for sean

Answer 12

k

Answer 13

whats for sean?

Answer 14

sean used (a-b)2=a2+b2-4ab, but d correct identity is (a-b)2=a2+b2-2ab

Answer 15

just like in Algebrs

Answer 16

ty

Answer 17

anytime:)

Answer 18

k

Answer 19

next problem