Is triangle ADB congruent to triangle CDB by SAS, AAS, ASA, SSS, or HL? If segment AB is congruent to segment CB and segment BD bisects segment AC....

We are given
with and bisects at .

(1) Since AB=CB we know that angles A and C are congruent from the isosceles triangle
theorem. Also since is bisected at D, we have AD=CD so the
by SAS

(2) BD=BD by the reflexive property. Since AD=CD you could use
SSS.

(3) If you know that the median drawn from the vertex angle of an
isosceles triangle is also the angle bisector of the vertex angle, the altitude drawn from the
vertex angle, and the perpendicular bisector of the base then you could use any of AAS,ASA, or
H-L.