Final answer:
A set of line segments that satisfy the Pythagorean theorem can form a right triangle.
Step-by-step explanation:
A right triangle is a triangle that has one angle measuring 90 degrees.
In order for a triangle to be a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) must equal the sum of the squares of the other two sides.
Using the Pythagorean theorem, we can determine if a set of line segments can form a right triangle.
For example, a set of line segments with lengths 3, 4, and 5 can form a right triangle.
The squared length of the hypotenuse, 5, is equal to the sum of the squares of the other two sides, 3^2 + 4^2 = 9 + 16 = 25.
Similarly, a set of line segments with lengths 5, 12, and 13 can also form a right triangle.
The squared length of the hypotenuse, 13, is equal to the sum of the squares of the other two sides, 5^2 + 12^2 = 25 + 144 = 169.