The proof that ΔQPT ≅ ΔQRT is shown.

Given: SP ≅ SR

line segment

Prove: ΔQPT ≅ ΔQRT

Triangle P Q R is shown. Angle P Q R is cut by a perpendicular bisector to form midpoint T on side P R. Point S is on line Q S. Lines are drawn from points P and R to point S. Line segments P S and S R are congruent.

What is the missing reason in the proof?

Statements Reasons
1. SP ≅ SR 1. given
2. ST ⊥ PR 2. converse of the perpendicular bisector theorem
3. PT ≅ RT 3. ?
4. QT ⊥ PR 4. ST and QT name the same line.
5. QP ≅ QR 5. perpendicular bisector theorem
6. ΔQPT ≅ ΔQRT 6. HL theorem
definition of perpendicular bisector
definition of congruence
reflexive property
substitution property