To determine which triangles are congruent based on the provided diagram and the choices, we need to analyze the given congruence statements using the criteria for triangle congruence: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or HL (Hypotenuse-Leg for right triangles).

Analysis:

1. Observe the triangle markings for sides and angles.

   • $\triangle TWP$ and $\triangle HGD$ have matching side lengths and angles marked, suggesting they might be congruent.
   • Other triangle pairs require verification based on the arrangement and marking alignment.

2. Apply the congruence criteria:

   • Compare the sides and angles between pairs of triangles.
   • Check whether the correct correspondence of vertices is maintained.

Solution:

The correct congruence statement(s) depend on matching sides and angles. Based on the markings and alignment, the valid congruences are:

• $\triangle WPT \cong \triangle GDH$ because all corresponding sides and angles align correctly.

Would you like me to break down each option or analyze further?

Here are 5 related questions to deepen understanding:

1. How can you determine if two triangles are congruent using the SSS postulate?
2. What does "corresponding vertices" mean in triangle congruence?
3. How does the ASA postulate work compared to SAS for proving congruence?
4. Can you find any congruent triangles in real-life structures or objects?
5. What is the significance of congruence in geometric proofs?

Tip: Always label corresponding parts of the triangles clearly when applying congruence criteria to avoid confusion.