Answer
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Step 1
The Lewis structure for C$_2$H$_4$ is: \begin{array}{cccc} \mathrm{H}-\mathrm{C}=\mathrm{C}-\mathrm{H} \ \quad | \qquad \quad | \ \quad \mathrm{H} \qquad \quad \mathrm{H} \end{array} There are five electron domains around each carbon atom (four bonding pairs and one lone pair).
Step 2
For C$_2$H$_4$, the electron domains are arranged in a trigonal bipyramidal geometry.
According to the VSEPR theory, the molecular geometry is determined by the arrangement of the electron domains. However, since there are no lone pairs on the central carbon atoms, the molecular geometry is reduced to a planar geometry with 120 -degree bond angles.
Final Answer
The molecular geometry of C$_1$H$_1$ is planar with a linear shape around each carbon atom.
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