We have to prove that ABDC is a parallelogram.
3) The third step is the reflexive property, where BD = BD (equal to itself). This let us to the following step, where we state that the 2 triangles are congruent.
4) Triangle ABD is congruent to triangle CBD, by the SSS postulate.
5) <1 = <3, as they are alternate interior angles between parallels.
6) <2 = <4, as they are alternate interior angles between parallels.
7) AB || CD
8) AD || BC
9) ABCD is a parallelogram as its opposite sides are congruent.