1. **Problem Statement:** In triangle $\triangle ABC$, the angle bisectors of $\angle A$ and $\angle B$ intersect at point $I$ inside the triangle. We need to determine which statement about point $I$ is always true. 2. **Key Concept:** The point where the angle bisectors of a triangle intersect is called the **incenter**. The incenter is equidistant from all sides of the triangle. 3. **Explanation of Options:** - "I lies on side AB": The incenter lies inside the triangle, not necessarily on any side. - "I lies on the perpendicular bisector of AB": The incenter is not generally on the perpendicular bisector of any side. - "I is equidistant from sides AB and AC": Since $I$ is the incenter, it is equidistant from all sides, including $AB$ and $AC$. - "I is the centroid of $\triangle ABC$": The centroid is the intersection of medians, not angle bisectors. 4. **Conclusion:** The correct statement is: $$\text{I is equidistant from sides } AB \text{ and } AC.$$