Let's analyze and solve the given problem step by step. --- ## Step 1: Understand the Problem The question asks: > Draw two geometrical isomers of 1,2-dimethylcyclohexane, C₈H₁₆, where each methyl group is attached to a different carbon of the cyclohexane ring, as indicated above. > > All hexagons should be more or less regular, with bonds at 120° angles. --- ## Step 2: Identify the Isomers **1,2-dimethylcyclohexane** means two methyl groups are attached to carbon 1 and carbon 2 of a cyclohexane ring. Cyclohexane rings can have **cis** and **trans** isomers when two substituents are on adjacent carbons. - **Cis isomer**: Both methyl groups are on the same side (both up or both down). - **Trans isomer**: One methyl group is up, the other is down. --- ## Step 3: Draw the Isomers ### **Cis-1,2-dimethylcyclohexane** - Draw a cyclohexane ring (hexagon). - Place a methyl group (CH₃) on carbon 1 (up). - Place a methyl group (CH₃) on carbon 2 (up, same side as carbon 1). ### **Trans-1,2-dimethylcyclohexane** - Draw a cyclohexane ring (hexagon). - Place a methyl group (CH₃) on carbon 1 (up). - Place a methyl group (CH₃) on carbon 2 (down, opposite side to carbon 1). --- ## Step 4: Illustrate the Isomers Here are the structures: ### **Cis-1,2-dimethylcyclohexane** ``` CH3 | / \ / \ | | \ / \ / CH3 ``` *Both methyls are on the same side (both up or down).* --- ### **Trans-1,2-dimethylcyclohexane** ``` CH3 | / \ / \ | | \ / \ / | CH3 ``` *The methyls are on opposite sides (one up, one down).* --- ## **Final Answer** **The two geometrical isomers of 1,2-dimethylcyclohexane are:** - **cis-1,2-dimethylcyclohexane** (both methyls on the same side) - **trans-1,2-dimethylcyclohexane** (methyls on opposite sides) These are the only two possible geometrical (cis/trans) isomers for 1,2-dimethylcyclohexane.