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enter image description here

I want to find if the above molecule shows cis-trans isomerism, per an assignment. I am assuming that such isomerism, if present, will be shown by the substituted chlorines.

It seems clear to me that the two chlorines in the picture lie in different planes. Therefore, the molecule will show optical isomerism, not cis-trans. However, the answer key says that it shows both optical and cis-trans isomerism.

I think the answer key is wrong. But if it is right, could someone please explain to me how this molecule shows cis-trans isomerism?

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    $\begingroup$ Please see duplicates, especially the second one. There isn't a clear answer, it's more of semantics / a technicality, rather than any real useful chemistry concept. $\endgroup$
    – orthocresol
    Jun 2 at 14:36
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    $\begingroup$ Just open the cyclohexane ring (similar to the pattern shown here and here) and apply the CIP rules to assign the double bond. Not evident from the drawing (missing wedges), though, is the configuration around the stereogenic centre. $\endgroup$
    – Buttonwood
    Jun 2 at 14:41
  • $\begingroup$ The ring is in the plane perpendicular to the double bond. Can you see now why it can show geometric isomerism? $\endgroup$ Jun 5 at 4:36