Which theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides?

Which theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides?

• A. Pythagorean Theorem
• B. Euclidean Theorem
• C. Calculus Theorem
• D. Trigonometric Theorem

Answer: (A)

The Pythagorean Theorem is the fundamental principle that relates the lengths of the sides in a right triangle. This theorem states that if you take the length of the hypotenuse (the side opposite the right angle) and square it, that value will be equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, this can be expressed as \(c^2 = a^2 + b^2\), where \(c\) represents the length of the hypotenuse and \(a\) and \(b\) represent the lengths of the other two legs of the triangle. This theorem is instrumental in various applications, including in construction, navigation, physics, and many areas of geometry, which underscores its significance in both theoretical and practical math. The relationship defined by the Pythagorean Theorem helps in determining distances and angles, which is key to solving problems involving right triangles.

The Pythagorean Theorem is the fundamental principle that relates the lengths of the sides in a right triangle. This theorem states that if you take the length of the hypotenuse (the side opposite the right angle) and square it, that value will be equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, this can be expressed as (c^2 = a^2 + b^2), where (c) represents the length of the hypotenuse and (a) and (b) represent the lengths of the other two legs of the triangle.

This theorem is instrumental in various applications, including in construction, navigation, physics, and many areas of geometry, which underscores its significance in both theoretical and practical math. The relationship defined by the Pythagorean Theorem helps in determining distances and angles, which is key to solving problems involving right triangles.