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?

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.