Question

To show that triangle TRK= triangle TUK by the SAS postulate, what additional information is necessary?

Answer 1

From the figure, we already have
RT = UT
and
TK = TK

Since these are already conditions for two sides being congruent, we only need an included angle to be congruent. So, the missing information is 
∠RTK ≅ ∠UTK