Explain a proof of Pythagorean Theorem using the image
Unfortunately, as an AI text-based model, I cannot directly see or interpret an image. However, I can explain a proof of the Pythagorean Theorem using a diagram.
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 consider a right-angled triangle ABC, where side AB is the hypotenuse. Draw a square with side length AB, and construct squares on the other two sides, AC and BC. You should now have three squares with sides AB, AC, and BC.
Next, draw lines connecting the corners of these squares to form two smaller squares and two small congruent rectangles within the larger square (see diagram).
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A _______|__|_______ C
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Now, consider the areas of these shapes. The area of the large square is (AB)^2 since all its sides have length AB.
The area of one of the smaller squares is (AC)^2, and the area of the other small square is (BC)^2. Thus, the combined area of these two squares is (AC)^2 + (BC)^2.
Within the large square, we can see that the area of the square with side length AB (hypotenuse) is equal to the combined area of the two smaller squares (AC)^2 + (BC)^2. Since the area of the large square is equal to the sum of the areas of the smaller squares, we have:
(AB)^2 = (AC)^2 + (BC)^2
This equation represents the Pythagorean Theorem, which confirms that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.