Here, according to the given figures, we can conclude that EF corresponds to E'F', ∠EDG Is-congruent-to ∠E'D'G', ∠DEF Is-congruent-to ∠D'E'F', and the transformation is a rigid transformation.
What are congruent sides?
When the sides of a figure are equal, the idea of congruent sides is employed in geometry.
What are congruent angles?
Congruent angles are those of equal measure.
What is a rigid transformation?
A rigid transformation is a plane transformation that preserves length.
What is isometric transformation?
An isometric transformation (or isometry) is a plane or shape-preserving transformation (movement). Isometric transformations include reflection, rotation, and translation, as well as mixtures of these, such as the glide, which combines a translation with a reflection.
How to solve this problem?
Notice that the parallelogram DEFG is mapped to D'E'F'G'. Clearly, DEFG and D'E'F'G' have the same sides and angles. So, EF corresponds to E'F', ∠EDG Is-congruent-to ∠E'D'G', and ∠DEF Is-congruent-to ∠D'E'F'. So, options 1, 3, and 4 are correct.
Here, FG and GD are adjacent sides, therefore they may not necessarily be congruent. So, FG does not correspond to G'D'. So, option 2 is incorrect.
From the definition of a rigid and isometric transformation, we can conclude that the transformation is a rigid and isometric transformation. So, option 5 is incorrect but option 6 is correct.
Therefore according to the given figures, we can conclude that EF corresponds to E'F', ∠EDG Is-congruent-to ∠E'D'G', ∠DEF Is-congruent-to ∠D'E'F', and the transformation is a rigid transformation. Hence options 1, 3, 4, and 6 are correct.
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