Question

Use the image to answer the question. Assess parallelograms  ADCB  and  EHGF  to decide if they are congruent. (1 point) Responses Yes, ADCB≅EHGF  because parallelogram ADCB was reflected. Yes,  upper A upper D upper C upper B congruent to upper E upper H upper G upper F  because parallelogram  upper A upper D upper C upper B was reflected. No, ADCB is not congruent to EHGF  because parallelogram ADCB was dilated. No,  upper A upper D upper C upper B is not congruent to  upper E upper H upper G upper F  because parallelogram  upper A upper D upper C upper B was dilated. Yes, ADCB≅EHGF  because parallelogram ADCB  was rotated. Yes,  upper A upper D upper C upper B congruent to upper E upper H upper G upper F  because parallelogram  upper A upper D upper C upper B  was rotated. Yes, ADCB≅EHGF  since parallelogram ADCB was translated. Yes,  upper A upper D upper C upper B congruent to upper E upper H upper G upper F  since parallelogram  upper A upper D upper C upper B was translated.

Answer 1

To determine if parallelograms ADCB and EHGF are congruent, we need to consider the types of transformations that can produce congruent figures. Congruent figures are those that have the same shape and size.

1. **Reflection**: If parallelogram ADCB was reflected, it would remain congruent because reflection preserves size and shape.
2. **Rotation**: If parallelogram ADCB was rotated, it would also remain congruent for the same reason.
3. **Translation**: If parallelogram ADCB was translated, it would still be congruent as translation also preserves size and shape.
4. **Dilation**: However, if parallelogram ADCB was dilated, it would not be congruent because dilation changes the size of the figure.

Based on the provided responses, the correct answer would depend on whether the transformation stated in the response is one that preserves congruence.

Given the validity of reflections, rotations, and translations in preserving congruence, the correct statements are:

- **Yes, ADCB ≅ EHGF because parallelogram ADCB was reflected.**
- **Yes, upper A upper D upper C upper B is congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was reflected.**

Based on the same logic, similar statements for rotation and translation would also be correct:

- **Yes, ADCB ≅ EHGF since parallelogram ADCB was translated.**
- **Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F since parallelogram upper A upper D upper C upper B was translated.**

However, without the specific image and the type of transformation applied to parallelogram ADCB, I cannot definitively choose the correct response. You would need to check the transformation to choose the correct option. If it was a reflection, rotation, or translation, then it is yes. If it was a dilation, then it is no.