Answer: AD=CD CPCTC
Check the entire explanation because I don't know which part it's asking for. Hope this helps!
Explanation:
We know BD bisects ABC and BD is perpendicular to AC
First of all, Angle ABD and Angle CBD are equal (definition of angle bisector)
Then, since BD is perpendicular to AC, which means it forms two 90 degree angles which are equal. (not sure about the reason)
Lastly, BD=DB (reflective property)
Now we know the triangles are equal by ASA (because a side is shared, and two angles touching that side are equal.
Through CPCTC (corresponding parts of congruent triangles are congruent) we know Triangle ABD and Triangle CBD are equal. This means AD=CD CPCTC