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Assess parallelograms and to decide if they are congruent.

(1 point)
ADCB EHGF
Yes, ADCB ≅EHGF because parallelogram ADCB was reflected.
Yes, ADCB ≅EHGF since parallelogram ADCB was translated.
No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated.
Yes, ADCB ≅EHGF because parallelogram ADCB was rotated

1 answer

To determine if parallelograms ADCB and EHGF are congruent, we need to understand the transformations that could have been applied to one parallelogram to obtain the other.

  1. Reflected: If parallelogram ADCB was reflected, it means that it is flipped over a line. This does not change the size or shape of the figure, and therefore, the two parallelograms would be congruent.

  2. Translated: Translation moves a figure without changing its shape or size, so if parallelogram ADCB was translated to get EHGF, they remain congruent.

  3. Dilated: Dilation changes the size of a figure. If parallelogram ADCB was dilated to obtain EHGF, they are not congruent since their sizes differ.

  4. Rotated: Rotation turns a figure around a point but does not change its size or shape. Therefore, if ADCB was rotated to become EHGF, they are congruent.

From this analysis, we can conclude:

  • If ADCB was reflected or translated or rotated, then ADCB ≅ EHGF.
  • If ADCB was dilated, then they are not congruent.

In conclusion, without knowing the specific transformation used, we can determine the following statements about their congruence:

  • "Yes, ADCB ≅ EHGF because parallelogram ADCB was reflected."
  • "Yes, ADCB ≅ EHGF since parallelogram ADCB was translated."
  • "Yes, ADCB ≅ EHGF because parallelogram ADCB was rotated."

Among the provided options, the answer would be one of the first three affirmations you highlighted. The last option, regarding dilation, is not correct.