Final Answer:
Parallelogram EFGH is the result of a Translation of parallelogram ABCD.
Step-by-step explanation:
In a translation, every point of the original figure moves the same distance and in the same direction.
The sides of parallelogram EFGH are parallel to the corresponding sides of parallelogram ABCD, and the corresponding angles are congruent. This consistency in both angles and sides indicates a translation.
Let's denote the vertices of parallelogram ABCD as A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), and D(x₄, y₄), and the vertices of parallelogram EFGH as E(x₁', y₁'), F(x₂', y₂'), G(x₃', y₃'), and H(x₄', y₄').
If we observe that the corresponding sides have the same length and the corresponding angles are equal, it implies a translation. Mathematically, the translation vector (Δx, Δy) can be obtained by subtracting the coordinates of a point in ABCD from its corresponding point in EFGH.
For instance, if we consider point A, (Δx, Δy) = (x₁' - x₁, y₁' - y₁). Applying this vector to all points in ABCD will provide the coordinates of EFGH.
In conclusion, the congruence of corresponding sides and angles in parallelograms ABCD and EFGH points towards a translation. The translation vector represents the direction and distance of the shift from one parallelogram to the other.
Therefore, parallelogram EFGH is the output of a translation of parallelogram ABCD.