Based on the given information and using the Angle Bisector Theorem and the Vertical Angles Theorem, we can prove that QRS is congruent to SRT.
To prove that QRS is congruent to SRT, we can use the Angle Bisector Theorem and the Vertical Angles Theorem.
Given:
- QT bisects SP
- SP bisects QT
- Triangles PQR and TSR meet at a common point R
To prove:
- QRS is congruent to SRT
Proof:
1. QT bisects SP and SP bisects QT, so we can conclude that SQ is congruent to ST (by the Angle Bisector Theorem).
2. Since PQR and TSR meet at a common point R, we know that angle PRQ is congruent to angle TRS (by the Vertical Angles Theorem).
3. Similarly, angle PQR is congruent to angle TSR (by the Vertical Angles Theorem).
4. From step 1, we know that SQ is congruent to ST.
5. By the Side-Angle-Side (SAS) congruence criterion, we can conclude that QRS is congruent to SRT.
Therefore, we have proven that QRS is congruent to SRT.