Which equation represents the Pythagorean theorem?

Which equation represents the Pythagorean theorem?

• A. a² + b² = c
• B. a + b = c²
• C. a² + b² = c²
• D. c² - a² = b²

Answer: (C)

The Pythagorean theorem is a fundamental principle in geometry that applies to right triangles. It states that 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. In the equation a² + b² = c², 'a' and 'b' represent the lengths of the two legs of the triangle, while 'c' represents the length of the hypotenuse. This relationship allows one to determine the length of any one side of a right triangle if the lengths of the other two sides are known. This concept is essential in various applications, including finding distances and solving real-world problems involving right triangles. The other equations listed do not accurately reflect the relationship described by the Pythagorean theorem, thus focusing on 'a² + b² = c²' is correct for expressing the theorem.

The Pythagorean theorem is a fundamental principle in geometry that applies to right triangles. It states that 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.

In the equation a² + b² = c², 'a' and 'b' represent the lengths of the two legs of the triangle, while 'c' represents the length of the hypotenuse. This relationship allows one to determine the length of any one side of a right triangle if the lengths of the other two sides are known.

This concept is essential in various applications, including finding distances and solving real-world problems involving right triangles. The other equations listed do not accurately reflect the relationship described by the Pythagorean theorem, thus focusing on 'a² + b² = c²' is correct for expressing the theorem.