Question

1. choose the definition or theorem with the correct words.

if a point in the interior of an angle is equidistant from both sides of the angle, then the point lies on the bisector of the angle.
equidistant
angle bisector theorem
converse of the perpendicular bisector theorem
converse of the angle bisector theorem

Explanation:

The Angle Bisector Theorem states that if a point is on the angle bisector, then it is equidistant from the sides of the angle. The given statement is the reverse (converse) of that. The Converse of the Angle Bisector Theorem says that if a point in the interior of an angle is equidistant from both sides of the angle, then the point lies on the bisector of the angle. The term "equidistant" is just a description (meaning equal - distance), not a theorem name. The Perpendicular Bisector Theorem and its converse are about perpendicular bisectors of line segments, not angle bisectors.

Answer:

Converse of the Angle Bisector Theorem