Question

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

Answer 1

Answer

The missing part is

    3.   perpendicular bisector theorem

Explanation

The proof that ΔQPT ≅ ΔQRT is shown.

Given: SP ≅ SR

Proof for : ΔQPT ≅ ΔQRT

Statements                            Reasons

1. SP ≅ SR                              1. given

2. ST ⊥ PR                            2. converse of the perpendicular bisector  

                                               theorem

3. PT ≅ RT                             3.   perpendicular bisector theorem

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