https://file.aiquickdraw.com/mathbot/file/1730377409829xvfm3iko.jpg

To determine if triangles \( \triangle ARC \) and \( \triangle DHT \) are congruent, let's analyze the information given in the image.

1. Both triangles show two pairs of congruent sides, indicated by tick marks.
2. Each triangle has a marked congruent angle, indicating angle \( \angle A \) in \( \triangle ARC \) is congruent to angle \( \angle D \) in \( \triangle DHT \).

With this setup, we can use the **SAS (Side-Angle-Side)** criterion for proving congruence because:
- We have two pairs of matching sides.
- There is a congruent angle between these sides.

Thus, the correct answer is:
- **A.** \( \triangle ARC \cong \triangle DHT \), by **SAS**.

Would you like further details, or do you have questions about congruence rules?

### Related Questions:
1. What are the criteria for triangle congruence other than SAS and SSS?
2. Why is the congruent angle between the two pairs of sides essential for SAS congruence?
3. How would the answer change if the angle was not between the two marked sides?
4. Can congruent triangles have corresponding angles that are not marked but are implied by other properties?
5. In what scenarios would SSS be the preferred criterion over SAS?

### Tip:
When determining congruence, always check if the marked angles and sides form a valid pair according to congruence criteria like SAS or SSS.

Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles by SSS or SAS, write 'not enough information'. Explain your answer.

Learn how to determine triangle congruence using SAS or SSS. This problem involves analyzing given triangles for congruent sides and angles to apply the correct congruence theorem. Suitable for students in Grades 8-10 studying geometric proofs.

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