Final answer:
Line segments that satisfy the Pythagorean theorem (a² + b² = c²) can create a right triangle. The set of line segments with lengths of 5 cm, 12 cm, and 13 cm meet this criterion, as 5² + 12² equals 13².
Step-by-step explanation:
To determine which set of line segments could create a right triangle, we need to apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse). The formula for this is a² + b² = c², where c represents the length of the hypotenuse and a and b are the lengths of the two legs.
Looking at the provided information, we have a specific example that illustrates the application of the Pythagorean theorem with the line segments of lengths 5 cm, 12 cm, and 13 cm. These segments would indeed form a right triangle, as 5² + 12² equals 13²:
- 5² = 25
- 12² = 144
- 13² = 169
The sum of the squares of the lengths of the two shorter sides, 25 and 144, equals 169, which is exactly the square of the length of the longest side (the hypotenuse, 13 cm). Therefore, line segments of lengths 5 cm, 12 cm, and 13 cm satisfy the Pythagorean theorem and can be used to create a right triangle.