The question asks what additional information is required to know if two triangles in the diagram are congruent using the Side-Angle-Side (SAS) theorem or postulate.

Side-Angle-Side (SAS) Congruence Theorem states that two triangles are congruent if:

1. Two sides of one triangle are congruent to two sides of another triangle.
2. The angle between those sides (the included angle) is congruent in both triangles.

In the diagram provided:

• We already see that segment $RS$ is shared by both triangles $QRS$ and $TRS$, meaning one pair of sides is congruent.
• The diagram indicates that $RQ \cong RT$, meaning we have a second pair of sides that are congruent.

What we need is the congruence of the included angle between these two sides in both triangles to satisfy the SAS postulate.

The angle that is between $RQ$ and $RS$ in $\triangle QRS$, and between $RT$ and $RS$ in $\triangle TRS$, is $\angle QRS \cong \angle TRS$.

Thus, Option 4, $\angle QRS \cong \angle TRS$, is the correct answer. This angle congruence completes the SAS postulate.

Would you like a more detailed explanation on the SAS postulate or any other aspects of triangle congruence?

Here are some related questions:

1. What is the definition of the SAS Congruence Theorem?
2. Can you explain other congruence postulates such as SSS or ASA?
3. How do shared sides help in proving triangle congruence?
4. What is an "included angle" in the context of the SAS postulate?
5. Why can't we use the other angle pairs given in the options for this problem?

Tip: Always ensure that the angle being used in SAS is the included angle between the two congruent sides for the postulate to hold.