∡T ≅ ∡T          reflexive property
∡SRT ≅ ∡RUT      both are right angles
ΔSTR ∽ ΔRTU      two angles congruent in each

   CPST

    Cross-multiplying

---

∡S ≅ ∡S          reflexive property
∡SRT ≅ ∡SUR      both are right angles
ΔSTR ∽ ΔSRU      two angles congruent in each

   CPST

      Cross-multiplying

  Equals added to equals

Factor out ST on the left side:



TU+SU = ST                     Whole = sum of parts

  Replacing equal by equal

   

Same as what you had to prove.

Edwin