Identification of a geometric theorem statement
Check the final answer first, then review the worked steps.
Problem
Identification of a geometric theorem statement
Answer
B. Converse of the Perpendicular Bisector Theorem
Step-by-step solution
- Analyze the statement: The problem presents a statement: "If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment." We need to identify which theorem this statement describes.
- Define the Perpendicular Bisector Theorem: The Perpendicular Bisector Theorem states that any point on the perpendicular bisector of a segment is equidistant from the segment's endpoints. This directly matches the given statement.
- Define the Converse of the Perpendicular Bisector Theorem: The Converse of the Perpendicular Bisector Theorem states that if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment. This is the reverse of the given statement.
- Define the Pythagorean Theorem: The Pythagorean Theorem relates the sides of a right triangle: $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. This is unrelated to the given statement.
- Define the Right Triangle Theorem: This is not a standard named theorem in geometry. It might refer to properties of right triangles, but not the specific statement given.
- Compare the statement to the definitions: The given statement perfectly matches the definition of the Perpendicular Bisector Theorem.
- Select the correct option: Based on the comparison, the statement describes the Perpendicular Bisector Theorem.