Identify the theorem described by the statement: If a point is on the bisector of a...
Check the final answer first, then review the worked steps.
Problem
Identify the theorem described by the statement: If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
Answer
D. Converse of the Angle Bisector Theorem
Step-by-step solution
- Analyze the statement: The statement says, "If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle." This is a conditional statement in the form "If P, then Q." Here, P is "a point is on the bisector of an angle," and Q is "it is equidistant from the two sides of the angle."
- Recall the Angle Bisector Theorem: The Angle Bisector Theorem states that if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. This is exactly what the given statement says.
- Consider the Converse of the Angle Bisector Theorem: The converse of a statement "If P, then Q" is "If Q, then P." So, the converse of the Angle Bisector Theorem would be: "If a point is equidistant from the two sides of an angle, then it is on the bisector of the angle."
- Compare the given statement with the theorems: The given statement directly matches the Angle Bisector Theorem. It is not the converse of the Angle Bisector Theorem, nor is it related to the Perpendicular Bisector Theorem (which deals with the bisector of a line segment).