Final answer:
Sophie carved the word 'LIAR' in the tree to express her feelings of anger and betrayal towards Tedros.
Step-by-step explanation:
Sophie carved the word 'LIAR' in the tree because she was angry at Tedros for not believing her. The tree was a symbol of their friendship, and Sophie wanted to convey her feelings of betrayal and hurt through the act of carving the word. This action served as a way for Sophie to express her emotions and to confront Tedros about his lack of trust.