Figure A Figure B
Which of the images above represents a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.
Based on the given images, Figure B represents a proof of the Pythagorean Theorem.
To explain why, let's first understand the Pythagorean Theorem: it 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 other two sides.
In Figure B, we can see three squares created on each side of the right-angled triangle. The smaller squares on the legs have areas equal to the squares of their corresponding side lengths. The larger square on the hypotenuse also has an area equal to the square of its length.
To prove the Pythagorean Theorem using Figure B, we can observe that the areas of the two smaller squares, when added together, give us the exact area of the larger square. In other words, the sum of the areas of the squares on the two legs is equal to the area of the square on the hypotenuse.
Mathematically, this can be expressed as:
a^2 + b^2 = c^2
Where 'a' and 'b' represent the lengths of the two legs, and 'c' represents the length of the hypotenuse.
By comparing the squares in Figure B, we can visually see that the theorem holds true, hence providing a proof of the Pythagorean Theorem.