In each figure below, the segments on the sides can be moved.Create the following triangles, if possible.First figure: A triangle with side lengths of 5, 7, and 8.Second figure: A triangle with side lengths of 2, 6, and 9.If there is no triangle possible with the given side lengths, click on "No triangle possible".

To determine if a triangle can be formed with given side lengths, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

1. For the first figure with side lengths of 5, 7, and 8:

   • 5 + 7 = 12, which is greater than 8
   • 5 + 8 = 13, which is greater than 7
   • 7 + 8 = 15, which is greater than 5 Therefore, a triangle can be formed with side lengths of 5, 7, and 8.

2. For the second figure with side lengths of 2, 6, and 9:

   • 2 + 6 = 8, which is less than 9
   • 2 + 9 = 11, which is greater than 6
   • 6 + 9 = 15, which is greater than 2 Because the sum of the lengths of the two shorter sides is not greater than the length of the longest side, a triangle cannot be formed with side lengths of 2, 6, and 9. Therefore, for this figure, click on "No triangle possible".