Roberto examines two molecular models. he sees that the atoms are the same in each model and are attached in the same order in each model. however, he cannot make the models appear the same without breaking a double bond. what do the models represent? two structural isomers that have the same molecular formula two geometric isomers that have the same molecular formula two organic compounds that have the same structural formula two models of a single organic compound

I have drawn the scenario as discussed in statement. The bond color shows their position before and after change. Structure 1 and 2 are those two models which are in hands of Roberto. These two structures are not identical to each other, as the blue and green bonds are not same (still the molecular formula of both compound is same). When structure 2 is broken at double bond, rotated at 180° degree and re assembled it forms the structure (3) exactly equal and same to structure 2.

Explanation:
                   It means that the positions of substituents are having different positions in space (3D). And we know well that the double bond can't be rotated as single bond. So, due to double bond rotation restriction we are having two isomers (such isomers which have different position in 3D are called Stereoisomers) and this stereoisomer which takes place due to double bond restriction is called Geometrical Isomerism or cis trans Isomerism.

Result:
           These two models (1 and 2) represent two geometric isomers that have the same molecular formula.