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Alkanes, alkenes, and alkynes are hydrocarbons that have various numbers of carbon-carbon (C-C) bonds. Alkanes have single C-C bonds, alkenes have at least one double C-C bond, and alkynes have at least one triple C-C bond.

Geometric isomerism is a form of stereoisomerism observed in molecules with a double bond or ring. In geometric isomers, the atoms are connected in the same order, but their spatial arrangement differs due to the restricted rotation of double bonds or rings.

In an alkene, there is at least one double bond between two carbon atoms (C=C). This double bond involves the sharing of four electrons between two carbon atoms. Due to the presence of this double bond, free rotation around the bond is not possible. The restricted rotation around the double bond gives rise to different spatial arrangements of atoms, leading to the possibility of geometric isomerism.

Alkanes have single carbon-carbon (C-C) bonds, which permit free rotation around these bonds. This free rotation allows for different arrangements of molecules to generate identical structures. Since the free rotation around single bonds does not lead to different spatial arrangements of atoms, geometric isomerism is not possible in alkanes.

Alkynes have carbon-carbon triple (C≡C) bonds. While triple bonds restrict rotation, geometric isomerism is still not possible for alkynes due to their linear structure. The carbons on either end of the triple bond and their directly attached atoms are all in a straight line, so there is no possibility for different spatial arrangements of atoms that would differentiate geometric isomers. In conclusion, geometric isomerism is possible for alkenes due to the restricted rotation around the double bonds and the ability for different spatial arrangements of atoms to form. In contrast, alkanes have free rotation around single bonds, and alkynes have a linear structure, both preventing varying spatial arrangements needed for geometric isomerism.