Question
If point R is the midpoint of both QS and PT, what additional information would you need to state that triangle PQR is congruent to TSR by the SAS Congruence Theorem?
Answers
GPT-4o mini
To state that triangle PQR is congruent to triangle TSR by the SAS Congruence Theorem, you would need the following additional information:
1. **The lengths of sides PQ and TS** should be equal: \( PQ = TS \).
2. **The lengths of sides QR and SR** should be equal: \( QR = SR \).
3. **The included angle between sides PQ and QR,** which is angle PQR, should be equal to the included angle between sides TS and SR, which is angle TSR: \( \angle PQR = \angle TSR \).
With this information, you could use the SAS (Side-Angle-Side) Congruence Theorem to conclude that triangles PQR and TSR are congruent.
1. **The lengths of sides PQ and TS** should be equal: \( PQ = TS \).
2. **The lengths of sides QR and SR** should be equal: \( QR = SR \).
3. **The included angle between sides PQ and QR,** which is angle PQR, should be equal to the included angle between sides TS and SR, which is angle TSR: \( \angle PQR = \angle TSR \).
With this information, you could use the SAS (Side-Angle-Side) Congruence Theorem to conclude that triangles PQR and TSR are congruent.