since by definition a parallelogram has two sets of opposite sides that are parallel and equal with each other, we can say that due to alternate angles, when we divide the parallelogram by its diagonal a pair of congruent angles appear like this
and due to alternate angles, we can also say that the corresponding angles will also be the same as this
Now since the diagonal is the same side for both triangles we can confirm that by the ASA theorem the two triangles are congruent.
![\begin{gathered} \text{statement 1:} \\ AD\parallel BC \\ \text{reason 1:} \\ \text{Definition of parallelogram} \\ \text{statement 2:} \\ DC\parallel BA \\ \text{reason 2:} \\ \text{Definition of parallelogram} \\ \text{statement 3:} \\ \measuredangle DAC=\measuredangle ACB \\ \text{reason 3:} \\ \text{alternate angles } \\ \text{statement 4:} \\ \measuredangle DCA=\measuredangle BAC \\ \text{reason 4:} \\ \text{alternate angles } \\ \text{statement 5:} \\ AC=AC \\ \text{reason 5: } \\ \text{common side} \end{gathered}]()
Then due to 3,4 and 5 triangles, ADC and ABC are congruent by ASA theorem.