Answer the questions based on the model and explain how it represents the Pythagorean Theorem.
What is the area of square A (a^2)?
What is the area of square B (b^2)?
What is the sum of areas of the squares (c^2)?
What is the square root of the sum of the areas of the squares (c)?
Explain how the diagram represents the Pythagorean Theorem.
The area of square A is a^2.
The area of square B is b^2.
The sum of the areas of the squares is c^2.
The square root of the sum of the areas of the squares is c.
The diagram represents the Pythagorean Theorem by showing that the square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides (a^2 + b^2). This can be seen visually as the areas of the squares labeled A and B, when added together, equals the area of the square labeled C. This relationship is at the core of the Pythagorean Theorem, which states 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.
Therefore, the diagram visually represents the Pythagorean Theorem by illustrating the relationship between the squares of the sides of a right-angled triangle.