Prove that triangle QRS is congruent to triangle STQ given line TS is congruent to line QR and line RS is congruent to line QT.

We are given quadrilateral QRST with:
(1) Segment QR congruent to segment ST is given
(2) Segment RS congruent to segment QT is given
(3) QS congruent to QS by the reflexive property of congruence
(4) Triangle QRS is congruent to triangle STQ by SSS (side-side-side congruence).
Note: SSS is a postulate or axiom in some texts. In others, SSS might be treated as a theorem (especially if the postulates are the isometric transformations).
See diagram:
http://mathworld.wolfram.com/SSSTheorem.html