Hello! I have a problem for school involving 2 column proof that I am close to solving, but can't seem to figure out entirely.

it's triangle ABC bisected by line BD

Given line BD is the perpendicular bisector of line AC, Prove line BD bisects angle ABC

this is what I put:

Step 1Line BD is the perpendicular bisector of line AC

Step 1Given

Step 2Line D is the midpoint of line AC

Step 2Definition of a perpendicular bisector

Step 3Line segment AD and line segment CD are congruent

Step 3Definition of midpoint

Step 4Line BD is perpendicular to line AC

Step 4Definition of a perpendicular bisector.

Step 5Angle ADB and CDB are right angles

Step 5Because they are on perpendicular lines

Step 6Angle ADB and CDB are congruent

Step 6Right angles are always congruent

Step 7Line BD is congruent to itself

Step 7Reflexive property

Step 8Line BD bisects angle ABC Step 8A bisector is a line which runs through the vertex of an angle and divides the angle into two congruent angles

my grader wrote back that "The proof is easy to follow and contains many logical steps and reasons. Revision of the last step and reasoning is needed to provide a sound logical conclusion. Congruence of triangles is mentioned but has not been clearly established."

Is anyone able to explain to me where I messed up with this? I thought I did it correctly, and I'm racking my brain here!