Solution
We have the following given:
BD bisects < ABC and BD is perpendicular to AC
From the info givenw e have this:
m < ABD = m < DBC (definition of bisector)
Since BD is perpendicular to AC then we have:
m < ADB = m < CDB (supplementary angle definition)
Then:
m < DAB= m < DCB (Because sum of angles in a triangle needs to be 180)
And then by AAA criteria triangle ADB is congruent with triangle CDB
