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

`\overline{ AZ}\cong \overline{AB}`

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).