Questions & Answers about היא גאה בי, ולכן היא מחייכת.
Because the subject is היא (she), and adjectives in Hebrew agree with the person they describe.
- masculine singular: גאה
- feminine singular: גאה
- masculine plural: גאים
- feminine plural: גאות
In this particular adjective, the masculine and feminine singular happen to look the same in writing, so you do not see a spelling change here. The feminine agreement is understood from the subject היא.
The adjective גאה commonly takes the preposition ב־ when you say who someone is proud of.
So:
- אני גאה בך = I am proud of you
- היא גאה בי = she is proud of me
Even though English uses of, Hebrew uses ב־ here. This is something you mainly have to learn as part of the expression להיות גאה ב־.