C is the incenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABC and DBC are congruent? It is given that C is the incenter of triangle ABD, so segment BC is an altitude of angle ABD.
Angles ABC and DBC are congruent according to the definition of an angle bisector.
Segments AB and DB are congruent by the definition of an isosceles triangle.
Triangles ABC and DBC share side BC, so it is congruent to itself by the reflexive property.
By the SAS postulate, triangles ABC and DBC are congruent.

Triangle ABD with segments BC, DC, and AC drawn from each vertex and meeting at point C inside triangle ABD.

There is an error in line 1; segment BC should be an angle bisector.
The proof is correct.
There is an error in line 3; segments AB and BC are congruent.
There is an error in line 5; the ASA Postulate should be used.