AFOQT Practice Test

The Pythagorean Theorem can be expressed as which equation?

1. a² + b² = c³

2. a² + b² = c²

3. a + b = 2c

4. a² + b² = c

The correct answer is: a² + b² = c²

The Pythagorean Theorem is a fundamental principle in geometry that applies to right triangles. It establishes a relationship between the lengths of the sides of such triangles, specifically stating that the sum of the squares of the two shorter sides (often referred to as 'a' and 'b') equals the square of the length of the longest side, which is known as the hypotenuse (represented as 'c'). This relationship is mathematically represented as a² + b² = c². The other options do not accurately represent this relationship. For example, one option incorrectly raises 'c' to the third power, which is not part of the Pythagorean Theorem. Another suggests a sum of the lengths rather than their squares, and one equates the sum of the squares of 'a and b’ with just 'c' without squaring it. Thus, the correct equation that defines the Pythagorean Theorem is indeed a² + b² = c².