Final answer:
The preposition 'over' fits the sentence, completing it as 'The arch over the hallway'. Arches are a key feature of Gothic architecture and can evoke memories of historical structures, such as the castles that likely inspired Natalie's recollection.
Step-by-step explanation:
The preposition that best completes the sentence "The arch ___ the hallway reminded Natalie of a castle she'd visited." is "over". In this context, "over" is used to indicate that the arch spans across the top of the hallway, much like those found in castles and other structures with Gothic architecture.
Arches are a prominent feature in various architectural styles, including the Gothic arches which are noted for their pointed shape. These are not only aesthetically pleasing but are also structurally advantageous because they allow for the efficient distribution of weight. This characteristic made them a common element in the cathedrals and castles of the Medieval period, which is likely why the arch reminded Natalie of a castle.
Not only do arches play a significant role in the structure and design of buildings, but they can also evoke emotions and memories, as seen in Natalie's association with a castle. This sentiment holds true in literature and art, where arches are often used to set the scene or invoke nostalgia for historical times.