FTCE General Knowledge Math Practice Test

What is the relationship between the hypotenuse and the other two sides in a right triangle?

1. Hypotenuse = Side 1 + Side 2

2. Hypotenuse = Side 1 - Side 2

3. Hypotenuse² = Side 1² + Side 2²

4. Hypotenuse² = Side 1² - Side 2²

The correct answer is: Hypotenuse² = Side 1² + Side 2²

In a right triangle, the relationship between the lengths of the hypotenuse and the other two sides is described by the Pythagorean theorem. This theorem 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. Mathematically, this is represented as hypotenuse² = side 1² + side 2². This relationship is foundational in geometry, particularly in the study of right triangles, and applies universally regardless of the specific measurements of the sides, as long as it is indeed a right triangle. The other options, although they suggest different mathematical relationships, do not accurately capture the essence of the Pythagorean theorem. For instance, a sum or difference of the lengths of the sides does not describe any standard relationship observed in right triangles. Thus, the correct relationship articulated by the Pythagorean theorem confirms that option C is the only one that accurately portrays how the hypotenuse relates to the other two sides in a right triangle.