Yes, it can be considered rude if someone invites you over for dinner and then starts eating without offering you anything or checking if you want something as well. In many cultures, hospitality and good manners dictate that hosts should be considerate and attentive to their guests' needs.
When inviting someone over for dinner, it is generally expected that the host will offer food and drinks to their guests, making sure they feel comfortable and well taken care of. This includes asking about dietary preferences or restrictions and accommodating them if possible. Starting to eat without extending this courtesy can be seen as impolite and inconsiderate.
Of course, there can be exceptions. For example, if the guests arrive significantly late, the host may begin eating to avoid the food getting cold. Or in some informal settings, close friends or family members may feel comfortable helping themselves without formalities. However, as a general rule, it is polite for the host to make an effort to include their guests in the meal and ensure everyone is taken care of.
If you find yourself in such a situation as the guest, and the host doesn't offer anything, it's perfectly acceptable to politely inquire about the meal or express your interest in what's being served. Communication is key, and sometimes people may not realize their oversight until it's brought to their attention. However, it's essential to approach the situation tactfully to avoid unnecessary discomfort or confrontation.