\#2) Which of the following sets could NOT be the sides of a right triangle? * 1 point \( 1,2,3 \) \( 3,4,5 \) \( 5,12,13 \) \( 6,8,10 \)

To determine which set of numbers cannot be the sides of a right triangle, we apply the Pythagorean theorem. This theorem states that in a right triangle, if the sides are a, b (legs) and c (the hypotenuse), then:   a² + b² = c² Let's examine each option: 1. For the set 1, 2, 3, assume the largest number (3) is the hypotenuse:   1² + 2² = 1 + 4 = 5   3² = 9 Since 5 ≠ 9, these do not satisfy the Pythagorean theorem. Additionally, 1 + 2 = 3, which means the sides would form a degenerate triangle. 2. For the set 3, 4, 5:   3² + 4² = 9 + 16 = 25   5² = 25 These satisfy the theorem. 3. For the set 5, 12, 13:   5² + 12² = 25 + 144 = 169   13² = 169 These satisfy the theorem. 4. For the set 6, 8, 10:   6² + 8² = 36 + 64 = 100   10² = 100 These satisfy the theorem. Thus, the set that could NOT be the sides of a right triangle is 1, 2, 3.