Question

what do you notice about these triangles with the same three side lengths? there is only one unique triangle are many different triangles are no possible triangles that can be made with these three side lengths.

Explanation:

The two triangles (and the third one implied) have the same three side lengths (7, 8, 10). By the SSS (Side - Side - Side) congruence criterion in geometry, if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. Congruent triangles have the same shape and size, but can be oriented differently. However, when we fix the three side lengths, there is essentially only one unique triangle (up to congruence) that can be formed because the side lengths determine the angles and the overall shape and size uniquely. The other options are incorrect: "are many different triangles" is wrong because SSS congruence shows they are congruent (so same triangle in terms of shape and size), and "are no possible triangles" is wrong as a triangle with sides 7, 8, 10 is valid (since 7 + 8>10, 7 + 10>8, 8 + 10>7, satisfying the triangle inequality theorem).

Answer:

is only one unique triangle