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When we are determining cis-trans isomerism, we seem to refer to a molecule's 'side' in relation to the double bond in a horizontal manner, as if we had drawn a mirror line through it horizontally. This lead us to say that the cis configuration of any molecule has atoms on the 'same side' of the double bond and a trans isomer on the 'opposite side' of the double bond.

If we had drew the line vertically and there was two species of the same type on one of the carbons in a double bond, this would then not exhibit isomerism as it would not have different groups attached, for example the arrangement in figure (2). But is there a geometric reason why we refer to the 'sides' in this way, or is it just convention as it necessarily must be this way?enter image description here

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    $\begingroup$ In case of (2), the two options are structural isomers (in the example, either a linear chain of four carbons or a chain of three carbons with a branch). The definition is such that if you could rotate around the double bond, trans and cis (or E and Z) would swap. On a different note, why does a mirror switch left and right and not top and bottom? $\endgroup$
    – Karsten ♦
    Apr 23, 2022 at 15:33

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You can still get isomers from "the other line"; it's just that they aren't cis/trans [or (E)-/(Z)-] isomers.

The reason why cis/trans isomers are "special" is that the molecular connectivity is the same. If you took the two isomers and looked solely at how each atom was bonded to which, while ignoring the 3D layout (the geometry) of the molecule, then the two isomers would be completely equal. This type of isomerism is called stereoisomerism, and cis/trans alkene isomers are one example of it.

On the other hand, if you were to swap a hydrogen and methyl on your alternative diagram, you would get a completely different connectivity with a linear instead of a branched carbon chain. The carbon on the left, instead of being doubly bonded to one carbon only, would now have a double bond to carbon and a single bond to carbon. These are still isomers, but they are structural isomers, not stereoisomers.

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