Based on the uploaded proof, here's how to fill in the missing parts:

Statements and Reasons:

1. SP ≅ TP, PQ bisects ∠SPT

   • Reason: Given

2. PQ ≅ PQ

   • Reason: Reflexive Property of Congruence

3. ∠SPQ ≅ ∠TPQ

   • Reason: Definition of Angle Bisector

4. △SPQ ≅ △TPQ

   • Reason: SAS Congruence Theorem

The proof demonstrates that △SPQ and △TPQ are congruent using the Side-Angle-Side (SAS) theorem.

Questions:

1. What is the importance of the Reflexive Property of Congruence in this proof?
2. How does the definition of an angle bisector help establish congruence?
3. Why is the SAS Congruence Theorem used instead of other congruence theorems like SSS or ASA?
4. What are other ways to prove △SPQ ≅ △TPQ without the given information?
5. How can this proof be applied to real-world geometric problems?

Tip:

Always align the congruence statement (e.g., SAS, SSS, ASA) with the specific parts of the triangle that are being compared to avoid errors in reasoning.