Question

Shown here are the three essential steps in a proof of the Pythagorean theorem. Why is the color blue kept the same in all three steps?

1) Because the blue areas remain constant in size
2) Because the blue areas are converted to squares
3) Because blue is used on the edges of the squares
4) Because the blue regions never equal the other regions in size

Answer 1

The color blue is kept consistent in a proof of the Pythagorean Theorem to show that the areas represented by the color remain constant in size throughout the steps of the proof.

Step-by-step explanation:

The color blue is kept the same across all three steps in a proof of the Pythagorean Theorem to indicate a consistency in the areas being represented. The blue areas remain constant in size throughout the different steps of the proof, therefore option 1) 'Because the blue areas remain constant in size' is correct. The use of color helps to visually track corresponding areas in different configurations, emphasizing that the area of the square formed by the hypotenuse (c) is equal to the sum of the areas of the squares formed by the remaining two sides (a and b).

In trigonometry and mathematics in general, visual aids such as color coding are often used to help clarify the relationships between different parts of a problem or proof. The Pythagorean Theorem, a² + b² = c², is a foundational principle in geometry, and understanding its proof is enhanced by visual consistency. This makes it easier to follow the logic and connect the parts of the theorem, which states that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.