MATH SOLVE

2 months ago

Q:
# 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 ? A True or False

Accepted Solution

A:

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.