Assess paralelograms ADCB and EHGF to decide if they are congruent.

Question

(1 point)
• Yes, ADCB ~ EHGF because parallelogram ADCB was rotated.
O Yes, ADCB = EHGF since paralelogram ADC B was translated.
O Yes, ADCB ≥ EHGF because parallelogram ADC B was reflected.
O No, ADCB is not congruent to EHGF because paralelogram ADCB was dilated

Answer 1

To determine whether parallelograms ADCB and EHGF are congruent, we need to look at the possible transformations that might relate them.

1. Congruence: Two shapes are congruent if one can be transformed into the other through rotations, translations, or reflections, without changing their size or shape.

2. Assessing the options:

   • "Yes, ADCB ~ EHGF because parallelogram ADCB was rotated."
     • This indicates that ADCB could be turned to match EHGF. However, congruence requires not just similarity but also equality in dimensions, which isn't specified here.
   • "Yes, ADCB = EHGF since parallelogram ADCB was translated."
     • Translation preserves distances and angles, thus this would typically imply congruence if they have the same dimensions.
   • "Yes, ADCB ≥ EHGF because parallelogram ADCB was reflected."
     • Reflection also preserves congruence, so if ADCB was reflected to become EHGF, they would be congruent.
   • "No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated."
     • Dilation changes the size and therefore does not preserve congruence; this would imply they cannot be congruent.

Given these assessments, the most definitive options regarding congruence are the translations and reflections, as they maintain size and shape. However, if we consider the possible operations and their effects:

The best answers supporting congruence would be "Yes, ADCB = EHGF since parallelogram ADCB was translated." and "Yes, ADCB ≥ EHGF because parallelogram ADCB was reflected."

Among these, if you must choose one, the translation option indicates equal dimensions directly, which would be the strongest assertion of congruence.