Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which equation represents the Pythagorean theorem?

1. a + b = c

2. a² + b² = c²

3. 2a + 2b = c

4. ab = c²

The correct answer is: a² + b² = c²

The Pythagorean theorem is a fundamental principle in geometry that relates to right-angled triangles. It states that the square of the length of the hypotenuse (the side opposite the right angle, denoted as 'c') is equal to the sum of the squares of the lengths of the other two sides (denoted as 'a' and 'b'). This relationship is expressed mathematically as \(a² + b² = c²\). This equation establishes a clear connection between the sides of a right triangle, providing a method to calculate one side if the other two are known. It forms the basis for various applications in mathematics, such as determining distances in coordinate systems. The other choices do not accurately represent this relationship. The first option suggests a simple addition of the two sides, which does not account for the geometric properties of a right triangle. The third option indicates a linear relationship that lacks consideration for the nature of the triangle's sides. Lastly, the fourth option inaccurately implies a multiplicative relationship which does not reflect the theorem's essence. Thus, the correct formulation of the Pythagorean theorem is indeed represented by \(a² + b² = c²\).