Answer:
Triangle ABD is congruent to Triangle CBD because of ASA
Explanation:
BD bisects Angle ADC --> Given
Angle ADB = Angle CBD --> Def of angle bisector (A)
Side DB = Side DB --> Reflexive Property (S)
Line segment BD is perpendicular to Line segment AC --> Given
Angle DBA = Angle DBC --> Def of perpendicular angles (A)
Triangle ABD congruent to Triangle CBD --> ASA
Using Statement and Reason form, we see that the two triangles are congruent because of the congruency rule: ASA (Angle Side Angle)