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The question is asking what additional information is needed to prove that the triangles are congruent by the **ASA (Angle-Side-Angle)** congruence theorem.

To apply the ASA theorem, we need to establish that:
1. Two angles of one triangle are congruent to two angles of another triangle.
2. The included side (the side between these two angles) is congruent.

Looking at the two triangles (△LGT and △MNQ), you can already observe that:
- ∠L is congruent to ∠M (both are marked with a single arc),
- ∠T is congruent to ∠Q (both are marked with a double arc).

What remains to complete the ASA criterion is to confirm that the side **between these two angles** is congruent. The side between ∠L and ∠T in △LGT is **LG**, and the side between ∠M and ∠Q in △MNQ is **MN**.

Thus, the additional information required is that **LG is congruent to MN**, which corresponds to **option b**.

### Conclusion:
The correct answer is **b) LG is congruent to MN**.

Would you like a more detailed explanation on the ASA theorem or any further clarification?

Here are 5 related questions:
1. What is the difference between ASA and SAS (Side-Angle-Side) congruence theorems?
2. Can SSA (Side-Side-Angle) prove congruence?
3. What are the other triangle congruence theorems?
4. How would you prove congruence if no sides are congruent?
5. What real-life applications involve triangle congruence?

**Tip**: When proving triangle congruence, always identify the parts (angles and sides) that correspond between the two triangles and check if they meet the conditions of a congruence theorem.

What additional information is needed to prove that the triangles are congruent by ASA?

Determine the additional information required to prove that triangles △LGT and △MNQ are congruent using the ASA (Angle-Side-Angle) theorem. The problem involves identifying congruent angles and the included side for triangle congruence. Suitable for students in Grades 9-10.

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