Final answer:
The Pythagorean Theorem proves the relationship of side lengths in a right triangle, allowing for calculation of the hypotenuse when the lengths of the other two sides are known.
Step-by-step explanation:
The type of triangle proved by the Pythagorean Theorem is the right triangle. The Pythagorean Theorem 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), which can be expressed as a² + b² = c². If you know the lengths of any two sides, you can use this theorem to solve for the third.
For example, if you're given the lengths of the two legs of a right triangle, you can use the Pythagorean theorem to find the length of the hypotenuse by rearranging the equation to solve for c: c = √(a² + b²). This theorem is a fundamental principle in geometry and is widely applied in various fields, including physics, engineering, and architecture.