Use the image to answer the question. Explain a proof of the Pythagorean Theorem using the image. (4 points) BoldItalicUnderlineIncrease indentDecrease indentFormula keypad

Answer 1

To explain a proof of the Pythagorean Theorem using the given image, we can observe that it consists of a right-angled triangle with side lengths a, b, and c. The image also shows that the square formed using side a has an area of a^2, the square formed using side b has an area of b^2, and the square formed using side c has an area of c^2.

Now, by rearranging the squares formed using side a and side b, we can notice that they can perfectly fit inside the square formed using side c. This implies that the total area of the two smaller squares (a^2 + b^2) is equal to the area of the larger square (c^2).

And this can be mathematically expressed as:

a^2 + b^2 = c^2

This is the equation of the Pythagorean Theorem, which states that in any right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Thus, the image visually illustrates the proof of the Pythagorean Theorem.