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
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
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 rotated.

Answer 1

To determine if the parallelograms ADCB and EHGF are congruent, we need to assess the transformations that relate them to each other. Congruent figures can be obtained from one another through transformations such as translation (sliding), reflection (flipping), or rotation (turning), but not through dilation (scaling), which changes the size.

Based on the options you provided, let's analyze them:

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

To choose the correct response, we need to recognize that if one parallelogram can be transformed into the other by reflection or rotation, then they are congruent. If any transformation mentioned is a dilation, then they are not congruent. Without seeing the actual image, it's impossible to assess these transformations directly.

If you can observe that the two parallelograms look identical in shape and size after applying a reflection or rotation, you would select one of the first or the last response options. If you notice a change in size, then you'd choose one of the options stating they are not congruent due to dilation. If they are simply shifted without changing size or orientation, you would select one of the responses regarding translation.

Given the context you've provided, if we assume that the only transformations happening are reflections or translations and these preserve size, you would lean toward confirming congruence. If dilation is occurring, you would select responses that state non-congruence.

Ultimately, you'll need to evaluate the image yourself to identify if the quadrilaterals were reflected, rotated, or translated, and then select the appropriate answer based on that analysis.