The missing reasons in the proof are as follows: 3. Congruent sides have congruent corresponding angles. 4. Congruent angles have congruent corresponding sides.
Here is the explanation why these statements fit the missing reasons:
1. The givens tell us that QT and OR are congruent, and that TR and TR are congruent.
2. Vertical angles are always congruent, so ZPRO and SRT must also be congruent.
3. Congruent sides have congruent corresponding angles, so APRO and ASRT must also be congruent.
4. Congruent angles have congruent corresponding sides, so PR and SR must also be congruent.
Therefore, the completed proof is as follows:
Statement | Reasons
1. QT = OR and TR = TR | 1. Given
2. ZPRO = SRT | 2. Vertical angles are congruent.
3. APRO = ASRT | 3. Congruent sides have congruent corresponding angles.
4. PR = SR | 4. Congruent angles have congruent corresponding sides.