SOLUTION: I have an image that is a Triangle with a line from the top angle to the middle line on the bottom: Given: Line segment BD is perpendicular bisector of line segment AC Prove: L

Question 821377: I have an image that is a Triangle with a line from the top angle to the middle line on the bottom:
Given: Line segment BD is perpendicular bisector of line segment AC
Prove: Line Segment BD bisects Angle ABC
I have tried to complete this task, but seem to be stuck on if I am doing so correctly and the right steps on how to achieve this proof.
Statement Reason
Angle BDA and Angle BDC are right angles. Definition of perp. lines.
Angle BDA is congruent to Angle BDC. Right Angle Theorem.
Line Segment AD is congruent to line segment DC. Definition of segment bisc.
Line segment BD is congruent to line segment BD. Reflexive Property.
Triangle ADB is congruent to triangle CDB. SAS.
Line segment AB is congruent to line segment CB. CPCTC.
Line segment BD bisects angle ABC. CPCTC.
I am unsure if I am correct in getting to this answer, as I tried to utilize all theorems and properties I could relate to this problem. Please help me fix where I am wrong, so I can accomplish my task.
Thanks
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You do not need
Line segment AB is congruent to line segment CB. CPCTC.
What I would say instead is
Angle ABD is congruent to Angle CBD. CPCTC.
Line segment BD bisects angle ABC. Definition of angle bisector.
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