Question 1098687
{{{ drawing(400,400, -5,5, -3, 5, 
         line(-2, 0, 2, 0),
        locate(-2.4,0, "A"),
        locate(2.2,0, "C"),
        line(0,0, 0,4), 
        locate(0.1, 4.2, "B"),
        locate(0, -0.2, "D"),
        red(line(-2,0,0,4)),
        red(line(0,4,2,0))
   )       
}}}

Angle ADB = Angle CDB = 90 degrees  (by construction, "BD is perpendicular to line AC")
Length AD = Length DC     (by construction, "BD bisects AC")
Length BD = Length BD    (common side)
By SAS (side-angle-side),  triangle ADB is congruent to triangle CBD.