Answer:
1. [tex]\Delta ABD\cong \Delta CDB[/tex] by SAS postulate.
Step-by-step explanation:
We have been given a figure of two triangles and we are asked to prove the given triangles are congruent.
We can see from our given figure that side length AB is equal to side length CD.
We can also see that [tex]m\angle CDB=m\angle ABD[/tex].
In triangles ABD and CDB side BD (common side) equals to itself.
So in triangle ABD and CDB two corresponding side lengths and their including angles are equal, therefore, [tex]\Delta ABD\cong \Delta CDB[/tex] by Side-Angle-Side congruence and 1st option is the correct choice.
