Here are the sentences completed with the correct articles:
1. In the United States, it is common to exchange gifts during the holiday season.
2. An important tradition in many cultures is to celebrate the New Year with fireworks.
3. Vietnamese New Year is celebrated with the giving of red envelopes containing money. (No article needed)
4. He's an honest man who always tells the truth.
5. A popular tradition in Ireland is to have a big family dinner on Christmas Day.
6. The wearing of green on St. Patrick's Day is a tradition that originated in Ireland. (No article needed)
7. In Japan, it is customary to bow when greeting someone. (No article needed)
8. An important custom in many weddings is for the bride to wear a white dress.
9. An apple a day keeps the doctor away.
10. The Eiffel Tower is one of the most famous landmarks in the world.