Question

Using the Pythagorean Theorem, which of the following is true?

A
The sum of the areas of squares B and C is

equal to the area of square A.

B
The sum of the areas of squares A and C is

equal to the area of square B.

C
The sum of the areas of squares A and B is

equal to the area of square C.

D
The difference of the areas of squares A and

B is equal to the area of square C.

Answer 1

The Pythagorean Theorem states that in a right triangle, the sum of the areas of the squares on the two legs (sides A and B) is equal to the area of the square on the hypotenuse (side C). This can be expressed mathematically as:

\[ A^2 + B^2 = C^2 \]

Where:
- \( A \) and \( B \) are the lengths of the legs of the right triangle,
- \( C \) is the length of the hypotenuse.

Given the options you've presented:

- **Option A** states that the sum of the areas of squares B and C equals the area of square A. (Incorrect)
- **Option B** states that the sum of the areas of squares A and C equals the area of square B. (Incorrect)
- **Option C** states that the sum of the areas of squares A and B equals the area of square C. (Correct)
- **Option D** states that the difference of the areas of squares A and B is equal to the area of square C. (Incorrect)

Thus, the correct answer is:

**C: The sum of the areas of squares A and B is equal to the area of square C.**