To determine if parallelograms ABCD and EHGF are congruent, we need to consider whether they can be related by any rigid transformations (reflections, rotations, or translations) that preserve their size and shape.
However, the mention of dilation in option b introduces a transformation that does change the size of the shape, thus affecting congruence.
Let's analyze each option:
a. Yes, ADCB≅EHGF because parallelogram ADCB was reflected.
- Correct: Reflection preserves the size and shape, so the two parallelograms would be congruent.
b. No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated.
- Correct reasoning: Dilation changes the size, so if ADCB was dilated, they would not be congruent.
c. Yes, ADCB≅EHGF because parallelogram ADCB was rotated.
- Correct: Rotation preserves size and shape, so if ADCB was rotated, the two would be congruent.
d. Yes, ADCB≅EHGF since parallelogram ADCB was translated.
- Correct: Translation preserves size and shape, so if ADCB was translated, the two would be congruent.
Given the analysis, we can summarize that options (a), (c), and (d) all support the claim of congruence due to rigid transformations (reflection, rotation, translation).
Thus, the best answers would be:
- a. (if reflection specifically occurred)
- c. (if rotation specifically occurred)
- d. (if translation specifically occurred)
Option b is definitely correct in stating that dilation would preclude congruence, but the question asks which options support congruence.
So, the final assessment emphasizes that ADCB and EHGF would be congruent if they were related by reflection, rotation, or translation but not if dilation occurred.
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