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?

Answer 1

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.