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Is this SSS SAS ASA AAS HL or not congruent? And don't assume any measurements

The image shows two triangles, \( \triangle ABC \) and \( \triangle DBC \), that share the side \( BC \). Here is a breakdown of what the diagram suggests based on the markings:

- \( AB = DC \) (indicated by single tick marks).
- \( AC = DB \) (indicated by double tick marks).
- \( BC \) is a common side to both triangles.

These conditions match the **Side-Side-Side (SSS)** criterion for triangle congruence because all three sides of one triangle are equal to the corresponding three sides of the other triangle.

Thus, the two triangles are congruent by **SSS**.

Would you like more details or have further questions? Here are 5 related questions to expand on this:

1. How do we prove triangle congruence using the SSS criterion?
2. What are the properties of congruent triangles?
3. Can triangle congruence help in determining angles?
4. What is the significance of shared sides in triangle congruence?
5. How would the proof differ if only two sides and one angle were known?

**Tip:** Always ensure to look for shared sides and marked angles to check for congruence efficiently!

Learn how to identify triangle congruence using criteria such as SSS, SAS, ASA, AAS, or HL. This specific problem involves two triangles with equal corresponding sides, leading to congruence by the SSS criterion. Suitable for students in Grades 7-10.

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