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

Question

(1 point)
Responses

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.

Yes, ADCB≅EHGF because parallelogram ADCB was reflected.

Answer 1

To determine if the parallelograms ADCB and EHGF are congruent, we need to consider the transformations that preserve congruence. Congruent figures can be related by translations, rotations, and reflections. Dilation, on the other hand, changes the size of the figure and does not preserve congruence.

Given the options:

1. Dilated - This would imply that the two parallelograms are not congruent.
2. Rotated - Rotating a figure preserves its size and shape, so this would imply congruence.
3. Translated - Translating a figure also preserves its size and shape, implying congruence.
4. Reflected - Reflecting a figure preserves its size and shape, implying congruence.

From this analysis, the responses indicating dilations would not be correct. The responses indicating congruence due to rotation, translation, or reflection would be correct.

Therefore, the correct responses are:

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

Since the question asks to choose one option, you might select any of the above statements excluding the dilation option. If you want to focus on a specific transformation, the “rotated” response is a solid choice as it is a common means of demonstrating congruence.

Answer 2

which one is it?

Answer 3

The best response indicating congruence due to a transformation that preserves size and shape is:

Yes, ADCB≅EHGF because parallelogram ADCB was rotated.

This option clearly states that the two parallelograms are congruent through a rotation, which is a transformation that maintains their congruence.