Final answer:
The Pythagorean Theorem can be used to determine if a triangle is a right triangle by comparing the squares of the side lengths. If the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse), then the triangle is a right triangle.
Step-by-step explanation:
The Pythagorean Theorem can be used to determine whether a triangle is a right triangle. The theorem states that in a right triangle, the square of the length of the hypotenuse (labelled c) is equal to the sum of the squares of the lengths of the other two sides (labelled a and b). Therefore, to determine if a triangle is a right triangle, we can calculate the squares of the lengths of the sides and check if they satisfy the Pythagorean theorem.
For example, if we have a triangle with side lengths a = 3 units and b = 4 units, we can calculate a² + b² = 3² + 4² = 9 + 16 = 25. If the square of the length of the hypotenuse (c²) is also 25, then the triangle is a right triangle. If not, it is not a right triangle.
In this case, we can see that a² + b² = 3² + 4² = 25 and c² = 5² = 25. Since a² + b² = c², this is a right triangle.