Final answer:
Two signs with a side 36 inches long are not necessarily congruent unless they have all sides and angles that are identical. For regular polygons like squares with all sides and angles equal, two such signs would indeed be congruent. For other shapes, more information would be necessary to determine congruence.
Step-by-step explanation:
The question asks to explain why two signs that each have a side 36 inches long must be congruent. In geometry, congruent figures have the same size and shape. If two signs have at least one side that is the same length, they might not necessarily be congruent, as congruence depends on all sides and angles being identical. For example, two triangles with one equal side are not necessarily congruent unless they satisfy certain conditions, such as the Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) postulates. However, if the two signs are regular polygons (like squares) with all sides equal and all angles equal and one of their sides is 36 inches, then they are congruent because they both have equal corresponding sides and angles.
To provide a more precise answer, additional information about the shapes of the signs would be necessary. For instance, if the signs were squares, the presence of four equal sides and four right angles would mean that both signs are congruent squares. If the shapes were triangles, there would need to be more information about the other sides and the angles between them.