Final answer:
To determine if vertices form a right triangle, use the Pythagorean Theorem by checking if a² + b² = c² is true for the lengths of the sides. If given the angles, ensure one angle is exactly 90 degrees, as the angles of a right triangle must sum up to 180 degrees with one being a right angle.
Step-by-step explanation:
To determine if vertices form a right triangle, you can apply 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. First, calculate the lengths of the three sides using the distance formula if only vertices are given. Once you have the side lengths, check if the Pythagorean Theorem holds true for the combination of these sides. If one specific side squared is equal to the sum of the squares of the other two sides, then the triangle is a right triangle, and the side that was squared alone is the hypotenuse.
If you're given the angles of the triangle instead of the side lengths, you can use trigonometry. You need to know that the sum of the angles in any triangle is 180 degrees, and a triangle will only be a right triangle if one of its angles is exactly 90 degrees. For instance, if you're given two angles and find that one of them is 90 degrees, then it is indeed a right triangle.