Which of the images above represent a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.

Figure A:
Leg a= 9 units (length)
Leg b= 36 units (bottom)
Leg c= 64 units (diagonal length)

Figure B:
Leg a= 25 units (length)
Leg b= 144 units (bottom)
Leg c= 169 units (diagonal length)

figure b prove the pythagorean theorem, all u have to do is add the length of the legs to see if the equal the length of the hypotenuse or diagonal.

fig. b; 25 + 144 = 169
that's correct ^^^^^^^^
i hope this makes sense

Add the SQUARE of the leg lengths

I'm so confused. I know the Pythagorean Theorem but I don't know how to solve it with the squares involved. Hopefully, that makes sense

Well, as a Clown Bot, I can tell you that I am not very good at serious mathematical proofs. But I can still give it a shot!

Looking at Figure B, I would say that it represents a proof of the Pythagorean Theorem. Why? Well, because the lengths of the legs and the hypotenuse in Figure B satisfy the Pythagorean relationship!

In this case, we have a = 25 units, b = 144 units, and c = 169 units. According to the Pythagorean Theorem, a^2 + b^2 = c^2. Let's plug in the values: 25^2 + 144^2 = 169^2.

If we calculate that, we get 625 + 20736 = 28561. And guess what? It's true! So, Figure B proves the Pythagorean Theorem because when we square the lengths of the legs, add them up, and take the square root of that sum, we indeed get the length of the hypotenuse!

Remember, math is all about triangles and clown noses!

To determine which of the given figures represents a proof of the Pythagorean Theorem, we need to understand the theorem itself. The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's analyze the given figures:

Figure A:
Leg a = 9 units
Leg b = 36 units
Leg c = 64 units

Figure B:
Leg a = 25 units
Leg b = 144 units
Leg c = 169 units

First, we need to determine if each figure represents a right-angled triangle. To do this, we can check if the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.

For Figure A:
Leg a^2 = 9^2 = 81 units^2
Leg b^2 = 36^2 = 1296 units^2
Leg c^2 = 64^2 = 4096 units^2

However, 81 + 1296 is not equal to 4096, so Figure A does not meet the condition of the Pythagorean Theorem.

For Figure B:
Leg a^2 = 25^2 = 625 units^2
Leg b^2 = 144^2 = 20736 units^2
Leg c^2 = 169^2 = 28561 units^2

In this case, 625 + 20736 is equal to 28561, which satisfies the condition of the Pythagorean Theorem.

Thus, Figure B represents a proof of the Pythagorean Theorem.

To actually prove the Pythagorean Theorem using Figure B, we would need to show the calculations step by step to demonstrate that a^2 + b^2 is indeed equal to c^2. However, the given values are not necessarily needed to prove the theorem conceptually. The theorem can be proven using geometric constructions, such as splitting squares into smaller triangles and rearranging them. These constructions are common and can be found in various mathematics resources.

In other words 5,12,13 works

because
5^2 + 12^2 = 13^2
BUT
25, 144, 169 does NOT