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Two quadrilaterals, upper A (-6,1) upper B (-3,1) upper C (-2,3) upper D (-5,3) and upper E (2,3) upper F (5, 3) upper G (6,5) upper H (3,5), 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 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 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.

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.

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.
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1 answer

To assess whether the two parallelograms ADCB and EHGF are congruent, we need to check their properties.

For parallelograms to be congruent, they must have the same shape and size. This can happen through transformation techniques like rotation, reflection, or translation, but not dilation, as dilation changes the size of the figure.

  1. Identifying the coordinates:

    • Parallelogram ADCB has vertices A (-6, 1), D (-5, 3), C (-2, 3), B (-3, 1).
    • Parallelogram EHGF has vertices E (2, 3), H (3, 5), G (6, 5), F (5, 3).

  2. Check lengths of sides and angles:

    • Calculate the lengths of the sides and angles of both parallelograms to confirm if they are identical.

  3. Transformation:

    • If one can be transformed into the other using rotation, reflection, or translation, then they can be considered congruent.

Based on your options, if parallelogram ADCB is congruent to EHGF through rotation or reflection without changing the size, then select:

Yes, ADCB≅EHGF because parallelogram ADCB was rotated. or Yes, ADCB≅EHGF because parallelogram ADCB was reflected.

If the figures are not the same size or shape, select:

No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated.

Since I do not have the exact measurements and properties of these specific parallelograms (as I can't see the image), you would need to make that determination based on the calculations you perform on their sides and angles.