Which of the following is the Angle Bisector Theorem?

A. 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.
B. If a point is in the interior of an angle and proportional from the two sides of the angle, then it lies on the bisector of the angle.
C. If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
D. If a point is on the bisector of an angle, then it is proportional from the two sides of the angle.

Answer: The answer is (B) If a point is in the interior of an angle and proportional from the two sides of the angle, then it lies on the bisector of the angle.

Step-by-step explanation: We are given four statements out of which we are to select the one which states the Angle Bisector Theorem.

The Angle Bisector Theorem states that an angle bisector of an angle of a triangle divides the opposite side in two segments which are proportional to the other two sides of the triangle.

Since the theorem matches with the statement (B), so the correct option is (B).