Answer:
The correct option is A. The given statement is true.
Step-by-step explanation:
Given statement: If A and B are two points in the plane , the perpendicular bisector of AB is the set of all points equidistant from A and B.
Let a line is perpendicular bisector of AB at point D and C be a random point of perpendicular bisector.
In triangle ACD and BCD,
[tex]AD=BD[/tex] (Definition of perpendicular bisector)
[tex]\angle ADC=\angle BDC[/tex] (Definition of perpendicular bisector)
[tex]DC=DC[/tex] (Reflexive property)
By SAS postulate of congruence,
[tex]\triangle ACD\cong \triangle BCD[/tex]
The corresponding parts of congruent triangles are congruent.
[tex]AC\cong BC[/tex] (CPCTC)
[tex]AC=BC[/tex]
The distance between A to C and B to C are same. So, the set of all points on perpendicular bisector are equidistant from A and B.
The given statement is true. Therefore the correct option is A.
