"danny draws a transversal, t, on two parallel lines ab and cd, as shown below.
he makes the following table to prove that the alternate interior angles are equal. "

It seems that you have missed the necessary options for this question, but anyway, here is the answer. So based on the given tables and figures above made by Danny proving that the alternate interior angles are equal, the missing justification would be that the corresponding angles formed by a transversal on parallel lines are congruent. Hope this answer helps.