Question

AC is the perpendicular bisector of ZB. What can you predict about AZ and AB

Answer 1

You can predict that line az and line ab are congruent

Answer 2

Answer:

$\overline{ AZ}\cong \overline{AB}$

Step-by-step explanation:

Given : AC is the perpendicular bisectore of ZB

i.e$\overline{OB}=\overline {OZ}$

In $\triangle AOB \;and \;\triangle AOZ$

OA=OA

By reflexive property of equality

OB=OZ

AC is a perpendicular bisector of BZ.

$\angle AOB=\angle AOZ$

Because AC is perpendicular to BZ

$\therefore$  $\triangle AOB\cong \triangle AOZ$

By SAS (Side-Angle-Side) postulate

$\overline{AB}\cong \overline{AZ}$

By CPCT( corresponding parts of congruent triangles are congruent).