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The problem in the image asks for a flowchart that shows the argument that two triangles are congruent, and to provide a sequence of transformations to map one triangle onto another.

The diagram depicts two triangles \( \triangle ABC \) and \( \triangle EDC \), which appear congruent. The markings on the triangles indicate that:
- \( \overline{AC} = \overline{EC} \) (matching sides),
- \( \overline{BC} = \overline{DC} \) (matching sides),
- \( \overline{AB} = \overline{ED} \) (matching sides).

These sides are equal, which hints that the two triangles are congruent by the **SSS (Side-Side-Side) Congruence Theorem**.

### Sequence of Transformations:
To map \( \triangle ABC \) onto \( \triangle EDC \), the following sequence of transformations could be applied:

1. **Reflection**: Reflect \( \triangle ABC \) across line \( \overline{CD} \), the perpendicular bisector of \( \overline{AB} \). This would position \( \triangle ABC \) over \( \triangle EDC \), ensuring the corresponding sides match.

2. **Translation**: Translate the reflected triangle along the line so that \( C \) coincides with \( C \), matching the vertices.

This sequence ensures that \( \triangle ABC \) maps perfectly onto \( \triangle EDC \), showing that the two triangles are congruent.

Would you like more details on the transformation steps or further explanations?

### Related Questions:
1. What are other congruence theorems that can prove two triangles are congruent?
2. Can you describe how to reflect a triangle across a line geometrically?
3. How does the SSS theorem compare to the SAS (Side-Angle-Side) theorem?
4. What is the difference between a translation and a rotation transformation?
5. How can we use coordinate geometry to prove congruence of triangles?

**Tip**: Always check if corresponding sides and angles are preserved in transformations to confirm congruence.

The problem in the image asks for a flowchart that shows the argument that two triangles are congruent and asks for a sequence of transformations to map one triangle onto another.

Understand how to prove two triangles are congruent using the SSS Congruence Theorem with a detailed flowchart and transformation sequence. This geometry problem is designed for students in Grades 7-10.

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