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To demonstrate that \( \triangle ABC \) and \( \triangle RST \) are congruent, we can analyze the transformations that would map \( \triangle ABC \) onto \( \triangle RST \).

### Sequence of Transformations
1. **Translation**: Move \( \triangle ABC \) such that point \( A \) maps to point \( R \). This aligns the triangles so that they share one corresponding point.

2. **Rotation**: After translation, rotate \( \triangle ABC \) around point \( R \) until line segment \( AB \) aligns with line segment \( RS \). This ensures that the orientation of the triangles matches and that the angle at point \( A \) aligns with the angle at point \( R \).

3. **Reflection (if necessary)**: If after rotation, the orientation of points \( B \) and \( C \) doesn’t match with points \( S \) and \( T \) (i.e., \( \triangle ABC \) is still not fully aligned with \( \triangle RST \)), reflect \( \triangle ABC \) across the line \( RS \). This will align all corresponding points and angles, demonstrating congruence.

These transformations (translation, rotation, and possibly reflection) show that \( \triangle ABC \) can be mapped exactly onto \( \triangle RST \), confirming their congruence.

Would you like more details on each transformation step or have any questions?

### Relative Questions:
1. How do we determine if a rotation or reflection is required to demonstrate congruence?
2. What properties of triangles confirm congruence after transformations?
3. Can congruence be demonstrated without using reflection in certain cases?
4. How does translation affect the orientation of a figure in the coordinate plane?
5. Why are transformations useful in proving congruence in geometry?

**Tip:** When examining transformations, always check if the sequence preserves distances and angles to ensure congruence.

Describe the sequence of transformations that was used to demonstrate that ΔABC and ΔRST are congruent.

Explore the sequence of transformations needed to demonstrate the congruence of triangles ABC and RST. Learn about translation, rotation, and reflection to align triangles in congruent positions. Ideal for students in Grades 8-10 studying geometric transformations.

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