TD = DC Property of a Rhombus (all four sides are equal)
<RDT = <FDC Vertically opposite angles are equal
ΔRDT ≅ ΔFDC Δ = triangle. The Δs are congruent by ASA.
RD = DF Parts of congruent triangles are congruent.
You will get problems like the way you were trying to do it. But you should just mark out what you know. I think that you might have forgotten about vertically opposite angles.