the congruence of the 2 triangles can be proved, angle C is common , CD is common, CA = CB, THEN the 2 triangles are congruent, the 2 triangles are equal so AD = DB hence CD bisects AB.
AND just that a attitude does not divides a line into equal half's, in an obtuse angle triangle the altitude is outside, only the median can divide a line into 2 equal half's or a triangle
hope this helps if this did Pls like and have any doubts ask me in the comments section, feel free