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Describe a series of rigid transformations for ABCD to reach figure EFGH 

To transform figure \( ABCD \) to match figure \( EFGH \) using a series of rigid transformations, we need to analyze their relative positions and orientations.

### Step-by-step Transformation:
1. **Translation**: Move \( ABCD \) so that point \( A \) coincides with point \( E \). This can be done by translating \( ABCD \) 4 units to the right and 2 units up, aligning the vertices \( A \) and \( E \).

2. **Rotation**: Rotate the translated figure around point \( E \) by 90 degrees clockwise. This will match the orientation of \( ABCD \) with that of \( EFGH \). For example, after rotation:
   - \( D \) will align with \( F \),
   - \( B \) will align with \( H \),
   - \( C \) will align with \( G \).

These two rigid transformations (a translation followed by a rotation) will map figure \( ABCD \) onto figure \( EFGH \).

Would you like more details on any of these transformations or how rigid transformations work?

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Here are 5 related questions to explore:
1. What are rigid transformations, and how do they preserve shape?
2. How do translations and rotations differ in geometry?
3. Can you describe a reflection that could also map \( ABCD \) onto \( EFGH \)?
4. How would you determine if two figures are congruent using transformations?
5. What properties of the two quadrilaterals suggest they are congruent?

**Tip**: Rigid transformations (translations, rotations, and reflections) do not change the size or shape of figures; they only change the position or orientation.

Describe a series of rigid transformations for ABCD to reach figure EFGH.

Learn how to map quadrilateral ABCD to quadrilateral EFGH using a series of rigid transformations, including translations and rotations. This problem explores congruence through geometric transformations, suitable for students in Grades 7-10.

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