In a right triangle, what is the hypotenuse?

In a right triangle, what is the hypotenuse?

• A. The shortest side
• B. One of the equal sides
• C. The longest side of the triangle
• D. The side opposite the right angle

Answer: (C)

In a right triangle, the hypotenuse is defined as the side opposite the right angle and is also the longest side of the triangle. This characteristic stems from the fundamental properties of right triangles, where one angle is exactly 90 degrees. According to the Pythagorean theorem, which applies to right triangles, the hypotenuse is always longer than either of the other two sides. This is because the relationship between the sides of a right triangle (the two legs and the hypotenuse) is such that the square of the hypotenuse equals the sum of the squares of the other two sides. By definition, no side in a right triangle can be shorter than the hypotenuse, ensuring it holds the title of the longest side. So, identifying the hypotenuse correctly as the longest side aligns perfectly with both geometric principles and algebraic relationships that govern right triangles.

In a right triangle, the hypotenuse is defined as the side opposite the right angle and is also the longest side of the triangle. This characteristic stems from the fundamental properties of right triangles, where one angle is exactly 90 degrees. According to the Pythagorean theorem, which applies to right triangles, the hypotenuse is always longer than either of the other two sides. This is because the relationship between the sides of a right triangle (the two legs and the hypotenuse) is such that the square of the hypotenuse equals the sum of the squares of the other two sides.

By definition, no side in a right triangle can be shorter than the hypotenuse, ensuring it holds the title of the longest side. So, identifying the hypotenuse correctly as the longest side aligns perfectly with both geometric principles and algebraic relationships that govern right triangles.