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DarlingDare
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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
 2 years ago
DarlingDare Group Title
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
 2 years ago

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DarlingDare Group TitleBest ResponseYou've already chosen the best response.0
Sean’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
 2 years ago

DarlingDare Group TitleBest ResponseYou've already chosen the best response.0
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.
 2 years ago

DarlingDare Group TitleBest ResponseYou've already chosen the best response.0
Please help
 2 years ago

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

myininaya Group TitleBest ResponseYou've already chosen the best response.3
Look 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
 2 years ago

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

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

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

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

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

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.3
For gina's
 2 years ago

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

DarlingDare Group TitleBest ResponseYou've already chosen the best response.0
Yes. 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.
 2 years ago

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

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

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

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.3
(ab)^2 is right
 2 years ago

DarlingDare Group TitleBest ResponseYou've already chosen the best response.0
(ab)(ab) ?
 2 years ago

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

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

DarlingDare Group TitleBest ResponseYou've already chosen the best response.0
ab, 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.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.3
1/2 *ab right?
 2 years ago

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

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.3
well 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?
 2 years ago

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

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

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

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

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

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

DarlingDare Group TitleBest ResponseYou've already chosen the best response.0
Ohhh..... whoops.
 2 years ago

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

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

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

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

DarlingDare Group TitleBest ResponseYou've already chosen the best response.0
You too!
 2 years ago
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