Use the image to answer the question.

Question

Two quadrilaterals, upper A upper B upper C upper D and upper E upper F upper G upper H, are graphed on a coordinate plane. The x-axis ranges from negative 7 to 7 in increments of 1. The y-axis ranges from negative 3 to 8 in increments of 1.

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

(1 point)
Responses

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.
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.
Skip to navigation

Answer 1

To determine if the two parallelograms, ABCD and EFGH, are congruent, we assess the transformations applied to parallelogram ABCD.

Congruent figures can result from translations, rotations, and reflections. Dilations, however, would change the size of the figure, which affects congruence.

Given the responses provided:

1. Yes, ADCB≅EHGF since parallelogram ADCB was translated.
2. Yes, ABCD congruent to EFGH since parallelogram ABCD was translated.
3. Yes, ADCB≅EHGF because parallelogram ADCB was reflected.
4. Yes, ABCD congruent to EFGH because parallelogram ABCD was reflected.
5. No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated.
6. No, ABCD is not congruent to EFGH because parallelogram ABCD was dilated.
7. Yes, ADCB≅EHGF because parallelogram ADCB was rotated.
8. Yes, ABCD congruent to EFGH because parallelogram ABCD was rotated.

To select the correct answer, one must identify how the first parallelogram (ABCD) was transformed into the second (EFGH). Since translations, rotations, and reflections preserve congruence, any of those transformations would lead to congruence.

Based on this reasoning, the correct responses could be the first four options, as they all mention transformations that maintain congruence (translations, rotations, and reflections).

If the transformation was actually a dilation, then the two shapes would not be congruent.

Overall, without visual confirmation from the image to confirm transformations, any options mentioning translations, reflections, or rotations would imply congruence. If dilation is indicated, then it conclusively states that the parallelograms are not congruent.

Conclusion: If there's evidence for transformation via translation, reflection, or rotation, choose either of those responses indicating congruence. If the transformation was dilation, opt for the corresponding response denying congruence.