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 2 years ago
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 + 4ab
Step 2: Area of triangle PKN =; hence the 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
 2 years ago
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 + 4ab Step 2: Area of triangle PKN =; hence the 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

This Question is Closed

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0Sean’s Proof: Step 1: Area of triangle EAF =; hence the area of 4 triangles = 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

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0Which 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.

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0May you help me? Please?????

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Look at one square at a time. Find the area of the bigger shape using the formula for area of square. Then find the area of the smaller shapes that are contained in the bigger shape. And then see if you get the Pythagorean thm c^2=a^2+b^2

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0So Sean's figure would be c^2, and Gina's figure would be (a+b)^2.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Ok those are the areas of the big shape that contains all the small shapes for each

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Now find the areas of the smaller shapes inside the big shapes

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0The square in Gina's figue would be c^2, and the triangles in Gina's figure will be 1/2 ab.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3and there are four of those triangles right?

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0And there are 4 triangles in Gina's figure so it would be 2 ab.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3\[bigger area=the \small \square+the triangles \]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Yep yep :) So we have \[(a+b)^2=c^2+2ab \text{ right?}\]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Now expand (a+b)^2 by writing (a+b)(a+b) and then distributing (or multiplying)

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. But, looking at the diagram, we know she isn't right, because she put 4 ab, instead of 2ab. So it's either Sean's right, or neither of them are right.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Ok yep you are right gina messed up there :)

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Ok now looking at sean's

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3you said the area of big square is c^2 right?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3now lets find the areas of the smaller shapes that are contained in this big square

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0Of the bigger square, yes.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3the area of the small square is?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Now tell me the area of on those triangle and then we will multiply it by 4 since there are 4 triangles

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3right (ab)^2=(ab)(ab) :)

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0ab, since on the hypotenuse, there are two different line segments on the same line which is ab+b, times b. or otherwise, a times b.

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0Yes... I forgot the 1/2 part... whoops. Thanks for helping me remember that! :)

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3And now there are four of those triangles so We have : for sean: c^2=4*1/2*ab+(ab)^2 bigsquare=thetriangles+smallsquare

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3\[c^2=4 \cdot \frac{1}{2} \cdot ab+(ab)^2\]

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0c^2 = 2ab + (ab)(ab) c^2 =2ab+ a^2 abab+b

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3well one little correction to what you have: c^2 = 2ab + (ab)(ab) c^2 =2ab+ a^2 abab+b^2 Step 3: Area of EFGH = c2 = Area of 4 triangles + area of ABCD = 2ab + a2 + b2 – 2ab And that is what he has for step 3 correct?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3mean because abab=2ab and so you have c^2=2ab+a^22ab+b^2

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0no... he's not correct, because he didn't have the a^2, or the negative sign in front of 2ab.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Hmmm then I must be looking at something different

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Are you sure? look again.

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0It says, "Step 3: Area of EFGH = c2 = Area of 4 triangles + area of ABCD = 2ab + a2 + b2 – 2ab Hence c2 = a2 + b2"

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3The ordering he has is a little different

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0Ok, then he's right. I just didn't see it correctly.... Thanks!!!

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3:) So how do you feel about this question? Do you understand it better?

DarlingDare
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. Thank you so very much!!!!!

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.3Np. Have a great day.
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