Answer
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Work Step by Step
Cis isomer is formed when two same groups are on the same side of the double bonded Carbons where as trans isomer is formed when two same groups are on the opposite side of the double bonded Carbons.
There is C-C single bond present in the compound 1,2-dichloroethane. We know that single bond is a $\sigma$ bond and this bond can rotate freely. So, for the compound 1,2-dichloroethane C-C bond free rotation possible. so, the compound will be the same after rotation.
On the other hand, for 1,2-dichloroethene there is $C=C$ double bond present. Double bond means one sigma and one pi bond. Between this, for $\pi$ bond to occur, the two orbitals must be parallel to each other. So, C=C double bond free rotation is not possible. In presence of high temperature, rotation of the double bond is possible. So, due to restricted rotation of the double bond, there are two compounds possible here as cis or trans isomer due to rotation of the double bond.
See the figure below.
