The short answer, that will go in the blank space, is ASA Property of Congruence
Here's how I got that answer:
We're at statement 5. Specifically we want the reason for why statement 5 is true. So we have to back up a few steps to look up at statement 3 and statement 4. With statement 3, we're proving that angle 2 and angle 5 are congruent, so are angles 1 and 4. So that takes care of two pairs of angles; hence the two "A" letters in ASA
Then in statement 4, we prove that BD is congruent to itself. There's not much to prove here as it is more like an axiom: any segment is congruent to itself through the reflexive property. This takes care of the "S" part in ASA
Putting that all together, we have two pairs of angles congruent with the pair of sides that are sandwiched between the angles. So that's why we use ASA
