Question

Which identity resulted from the proof in part A, which showed that a triangle with side lengths x² 1, 2x, and x² + 1 is a right triangle?

a. (x² 1)² (2x)² = (x² + 1)²
b. (x² 1)² + (2x)² = (x² + 1)²
c. (x² 1)² + (2x)² = (x² + 1)²
d. (x² 1)² + (2x)² = (x² + 1)²

Answer 1

The identity verifying that a triangle with side lengths x² - 1, 2x, and x² + 1 is a right triangle is (x² - 1)² + (2x)² = (x² + 1)², according to the Pythagorean theorem.

Step-by-step explanation:

The identity resulting from the proof in part A, which demonstrated that a triangle with side lengths x² - 1, 2x, and x² + 1 is a right triangle, is:

• (x² - 1)² + (2x)² = (x² + 1)²

This is derived using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². Applying this theorem to our triangle:

• (x² - 1)² represents the square of one leg.
• (2x)² represents the square of the other leg.
• (x² + 1)² represents the square of the hypotenuse.

Therefore, the identity confirms that the triangle with the given sides is indeed a right triangle.