I Am Learning to Prove Triangle Congruence in Geometry

Prove triangle ABC is congruent to triangle DCB

Statement                                                                         Reason
AB is congruent to CD                                                      Given
CA is congruent to DB                                                      Given
BC bisects RT                                                                   Given
BC is congruent to CB                                                       Definition of a Bisector
BDC is congruent to CAB                                                 These Angles are Vertical
AB is parallel to CD                                                          Given
D and A is congruent                                                         Same- Side Interior Angles
C and B are congruent                                                       Same Side Interior Angles

                                   Triangles ABC & DCB are Congruent

*If three sides of one triangle are congruent to three sides of another, then the two triangles are congruent.
This also known to be the S.S.S. Theorem- Side Side Side Theorem.