Question
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. 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 reflected.
Answers
Answered by
GPT-4o mini
To determine whether the parallelograms ADCB and EHGF are congruent, we need to consider the transformations that could have occurred between the two shapes.
Parallelograms are congruent if they can be made to coincide through rigid transformations, which include rotations, translations, and reflections. Dilation, however, changes the size of the shape and thus does not produce congruent shapes.
Given the provided options, the:
- statements identifying the shapes as congruent due to rotation, translation, or reflection would be valid.
- statements suggesting dilation are incorrect because dilation does not preserve congruence.
Based on this understanding, if parallelogram ADCB can be transformed into parallelogram EHGF through any rigid transformation (rotation, translation, or reflection), then the correct response would be:
**Yes, ADCB≅EHGF because parallelogram ADCB was rotated.**
or
**Yes, ADCB≅EHGF since parallelogram ADCB was translated.**
or
**Yes, ADCB≅EHGF because parallelogram ADCB was reflected.**
If there is a specific transformation you have in mind (like rotation, translation, or reflection), that would help in confirming congruence. However, at least one of the options acknowledging a rigid transformation leads to the conclusion of congruence.
Parallelograms are congruent if they can be made to coincide through rigid transformations, which include rotations, translations, and reflections. Dilation, however, changes the size of the shape and thus does not produce congruent shapes.
Given the provided options, the:
- statements identifying the shapes as congruent due to rotation, translation, or reflection would be valid.
- statements suggesting dilation are incorrect because dilation does not preserve congruence.
Based on this understanding, if parallelogram ADCB can be transformed into parallelogram EHGF through any rigid transformation (rotation, translation, or reflection), then the correct response would be:
**Yes, ADCB≅EHGF because parallelogram ADCB was rotated.**
or
**Yes, ADCB≅EHGF since parallelogram ADCB was translated.**
or
**Yes, ADCB≅EHGF because parallelogram ADCB was reflected.**
If there is a specific transformation you have in mind (like rotation, translation, or reflection), that would help in confirming congruence. However, at least one of the options acknowledging a rigid transformation leads to the conclusion of congruence.