For the first option, we have that AB = CD, which is a property of a paralellogram, so for this option the answer is k. parallelogram.
For the second option, we have AD = AD, which states that AD is equal itself, so this case we have the b. reflexive property of =.
For the third option, we have the SSS (side-side-side) case of congruency of triangles, so the best option for this case is a. △BAD = △CDA.
For the fourth option, we have △BAD = △CDA, which defines a congruency of triangles, therefore the correct option is f. SAS, which shows the case used for congruency.
For the sixth option, we have that two angles are supplementary, and we have an icon of a parallelogram, so the best option is j. consecutive ∠s supplementary.
For the seventh option, we have that the angles ∠BAD and ∠CDA are right angles, so the best option is e. right ∠s.