Shown here are the three essential steps in a proot of the Pythagorean Theorem. Companing the 1st and 3rd steps,how are the colored regions related as to areas? A yellow+blue=orange B orange=yellow+green C yellow+blue=green+orange D yellow+green=orarige+blue E orange+vellow+creen=blue+orange

#ExplanationThe 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. This can be written as: , where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.In the context of the given question, the colored regions represent the areas of the squares whose sides are the lengths of the sides of the right-angled triangle.From the first step, we can see that the area of the square with side length a (represented by the yellow region) plus the area of the square with side length b (represented by the blue region) equals the total area of the square.In the third step, the same total area of the square is now represented as the sum of the areas of two different regions: the area of the square with side length c (represented by the orange region) and the area of the four right-angled triangles (represented by the green region).Comparing the first and third steps, we can see that the sum of the areas of the yellow and blue regions (from the first step) equals the sum of the areas of the green and orange regions (from the third step). Therefore, the correct relationship between the colored regions in terms of their areas is: yellow + blue = green + orange.#AnswerC yellow + blue = green + orange