To determine whether parallelograms ADCB and EHGF are congruent, we need to consider the transformations that preserve congruence: translations, rotations, and reflections.
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Dilation does not preserve congruence because it changes the size of the shape; therefore, if ADCB was dilated to get EHGF, then they cannot be congruent.
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Translation maintains the shape and size of the figure, meaning if ADCB was translated to become EHGF, then they are congruent.
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Rotation also preserves shape and size, so if ADCB was rotated to become EHGF, then they are still congruent.
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Reflection preserves both the shape and size but may change the orientation. If ADCB was reflected to form EHGF, they would be congruent.
Based on the options provided, if we conclude that ADCB has undergone a reflection, rotation, or translation, then ADCB would be congruent to EHGF.
Thus, the correct answer would likely be "Yes, ADCB≅EHGF because parallelogram ADCB was reflected" if that were the case. However, if any transformation cited is true (translation, or rotation), the corresponding answer would also be correct.
Since we cannot definitively assess without more information regarding the transformations applied, it's best to select the answer that reflects a true congruence condition. If "ADCB was translated" or "ADCB was rotated" or "ADCB was reflected" are given as truths, then these statements would also be valid.
In summary, the answer could indeed vary depending on the transformation specified.
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