Answer:
[tex]\overline{ AZ}\cong \overline{AB}[/tex]
Step-by-step explanation:
Given : AC is the perpendicular bisectore of ZB
i.e[tex]\overline{OB}=\overline {OZ}[/tex]
In [tex]\triangle AOB \;and \;\triangle AOZ[/tex]
OA=OA
By reflexive property of equality
OB=OZ
AC is a perpendicular bisector of BZ.
[tex]\angle AOB=\angle AOZ[/tex]
Because AC is perpendicular to BZ
[tex]\therefore[/tex] [tex]\triangle AOB\cong \triangle AOZ[/tex]
By SAS (Side-Angle-Side) postulate
[tex]\overline{AB}\cong \overline{AZ}[/tex]
By CPCT( corresponding parts of congruent triangles are congruent).
