Since triangles ABD and ACD are congruent, it follows that "corresponding parts", such as angles BAD and CAD and angles BDA and CDA are congruent.

Lable the point of intersection "P". Now clearly AP is a line in both triangle ABP and triangle ACP. Use SAS to prove those two triangles are congruent.

Similarly, DP is a line in both triangle DBP and triangle DCP. Use SAS to prove those two triangles are congruent.