We have to find the reason for statement 3, which is:
[tex]m\angle ABD=m\angle CBD[/tex]
This angles are the angles that are formed after the bisection of ∠ABC.
As BD is an angle bisector, then the angle is divided into two equally measured angles, that are ∠ABD and ∠CBD.
Then, the reason for this statement is the definition of angle bisector.
Answer: definition of angle bisector [Option A]
