In order to prove that the triangles are congruent, we can write the following statements and reasons:
First box of the first row:
Statement: BD bisects angle ABC
Reason: Given
First box of the second row:
Statement: Angle ABD congruent to angle DBC
Reason: Definition of angle bisector
Second box of the second row:
Statement: angle ADB congruent to angle BDC
Reason: Given
Third box of the second row:
Statement: Side AB congruent to side BC
Reason: Given
Since we have two pair of corresponding angles and one pair of corresponding sides congruent, the triangles are congruent by case AAS.
