According to the Pythagorean Theorem, how are the sides of a right triangle related?

According to the Pythagorean Theorem, how are the sides of a right triangle related?

• A. a² + b² = c²
• B. c² = a² + b
• C. a² - b² = c²
• D. a + b + c = 180°

Answer: (A)

In the context of the Pythagorean Theorem, the relationship among the sides of a right triangle is expressed as a² + b² = c². In this equation, 'a' and 'b' represent the lengths of the two legs of the triangle, while 'c' represents the length of the hypotenuse, which is the side opposite the right angle. This theorem is a fundamental principle in geometry and applies specifically to right triangles, providing a means to calculate the length of one side if the lengths of the other two sides are known. The relationship demonstrates that the sum of the squares of the legs equals the square of the hypotenuse, establishing a clear and precise geometric relationship. Other options do not align with the established theorem. For example, the incorrect alternatives suggest relationships that either do not apply to right triangles or misrepresent the mathematical principles relating to these triangles. Understanding this foundational relationship is essential for solving various problems in geometry.

In the context of the Pythagorean Theorem, the relationship among the sides of a right triangle is expressed as a² + b² = c². In this equation, 'a' and 'b' represent the lengths of the two legs of the triangle, while 'c' represents the length of the hypotenuse, which is the side opposite the right angle.

This theorem is a fundamental principle in geometry and applies specifically to right triangles, providing a means to calculate the length of one side if the lengths of the other two sides are known. The relationship demonstrates that the sum of the squares of the legs equals the square of the hypotenuse, establishing a clear and precise geometric relationship.

Other options do not align with the established theorem. For example, the incorrect alternatives suggest relationships that either do not apply to right triangles or misrepresent the mathematical principles relating to these triangles. Understanding this foundational relationship is essential for solving various problems in geometry.