Can you prove DEFG is a parallelogram? Explain.(1 point)

Question

Responses

Yes, One set of sides is congrunet and the other set are parallel
Yes, One set of sides is congrunet and the other set are parallel

Yes. An angle of DEFG is supplementary to both of its consecutive angles.
Yes. An angle of DEFG is supplementary to both of its consecutive angles.

No. An angle of DEFG is not supplementary to both of its consecutive angles.
No. An angle of DEFG is not supplementary to both of its consecutive angles.

Answer 1

To prove that DEFG is a parallelogram, we can use several properties of parallelograms. Here are two adequate methods for proving DEFG is a parallelogram:

1. One Set of Opposite Sides is Parallel and Congruent: If one set of opposite sides is both parallel and congruent, then DEFG is a parallelogram. This response states: "Yes, one set of sides is congruent and the other set are parallel."

2. Consecutive Angles are Supplementary: If an angle of quadrilateral DEFG is supplementary to both of its consecutive angles, then DEFG is a parallelogram. This is confirmed by the response: "Yes. An angle of DEFG is supplementary to both of its consecutive angles."

Therefore, the correct responses to prove DEFG is a parallelogram are:

• "Yes. An angle of DEFG is supplementary to both of its consecutive angles."
• "Yes, one set of sides is congruent and the other set are parallel."

Both responses are valid, and based on either property, DEFG can be proven to be a parallelogram.