It looks like you've uploaded a geometric figure with some multiple-choice questions related to it. The diagram involves two segments $QT$ and $SU$ that bisect each other at point $R$.

The question asks which of the following must be true based on the given information. I'll analyze the options to help you choose the correct one.

Let me break it down:

• Since $QT$ and $SU$ bisect each other at $R$, we know that $QR = RT$ and $SR = UR$.
• We also know that vertical angles are congruent, so any vertical angles formed by the intersections of the two segments must be equal.

Now, let's analyze each option:

1. Option 1:

   • If $QT$ and $SU$ bisect each other at $R$, we get the relationships $QR = RT$ and $SR = UR$. From the bisecting property and the vertical angle congruence, the relationship $QR = TR$ and $SR = UR$ is not directly supported in this case.

2. Option 2:

   • This option correctly uses the fact that $QT$ and $SU$ bisect each other. Given vertical angle congruence, we can infer that angles $\angle QRU = \angle RST$, so the triangles formed are congruent based on the angle-side-angle (ASA) postulate, making this a valid choice.

3. Option 3:

   • This statement involves the congruence of sides $QU$ and $TR$. However, the congruence of these segments is not guaranteed directly by the given conditions.

4. Option 4:

   • This option also seems to be valid, but it focuses on angle congruence $\angle QRU = \angle RST$ and concludes that the triangles are congruent, supporting the choice similar to option 2.

Given the analysis, Option 2 seems to be the correct one.

Would you like further clarification on any specific step in the solution? Or do you have other questions about the problem?