Question

What are the missing parts that correctly complete the proof? Given: Point P is on the perpendicular bisector of segment AB. Prove: Point P is equidistant from the endpoints of segment AB.

a) Definition of bisector
b) Reflexive property of congruence
c) SAS congruence postulate
d) Corresponding parts of congruent triangles are congruent.

Answer 1

The missing part that correctly completes the proof is the definition of bisector. By definition, the perpendicular bisector of a segment is the line that intersects the segment at its midpoint and forms right angles with it. Therefore, any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Step-by-step explanation:

To prove that point P is equidistant from the endpoints of segment AB, we can use the property of the perpendicular bisector. Since point P is on the perpendicular bisector of segment AB, it means that point P is equidistant from the endpoints of segment AB.

The missing part that correctly completes the proof is: (a) Definition of bisector.

By definition, the perpendicular bisector of a segment is the line that intersects the segment at its midpoint and forms right angles with it. Therefore, any point on the perpendicular bisector is equidistant from the endpoints of the segment, which proves that point P is equidistant from the endpoints of segment AB.