The proof that ΔQPT ≅ ΔQRT is shown. Given: SP ≅ SR 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