The question is asking about the Angle Bisector Theorem. According to the Angle Bisector Theorem, if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. The correct answer matches this description:

• Correct Answer: C. "If a point is in the interior of an angle and equidistant from the two sides of the angle, then it lies on the bisector of the angle."

This is because the Angle Bisector Theorem specifically states that any point on the angle bisector is equidistant from both sides of the angle.

Would you like a deeper explanation of this theorem or examples of its application?

Here are some related questions:

1. What is the converse of the Angle Bisector Theorem?
2. How can you use the Angle Bisector Theorem to solve triangle problems?
3. What is the significance of the incenter in relation to angle bisectors?
4. Can the Angle Bisector Theorem be used in non-right triangles?
5. How does the Angle Bisector Theorem relate to the construction of a triangle’s incenter?

Tip: Remember, the Angle Bisector Theorem helps in determining equal distances from a point on the bisector to both sides of the angle, which is particularly useful in solving problems involving triangle centers.