Final answer:
The word 'obtrude' in the sentence is correctly used to denote the act of imposing oneself, against social norms, into a private event (like a birthday party) without an invitation indicating that such behavior is inappropriate.
Step-by-step explanation:
The vocabulary word being used in the sentence is 'obtrude', which means to impose or force oneself or one's ideas on others. The sentence is 'It is rude to obtrude on a birthday party by showing up without an invitation.' In this context, 'obtrude' is used correctly as it's referring to the inappropriate act of forcing oneself into an event, in this case, a birthday party, without an invitation, thereby disturbing the atmosphere and possibly the ongoing activities.
Important to note is the element of social agreements and expectations that underpin this situation. The person hosting the birthday party assumes the role of a host and expects guests to respect certain norms, including not showing up uninvited. This mirrors the context outlined in the information given where a host expects their guests to respect their property and rules.
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