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Which statements prove that a quadrilateral is a parallelogram?

Select each correct answer.

Responses

Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.
quadrilateral D E F G has one set of opposite sides that are both congruent and parallel.

Quadrilateral DEFG has only one set of opposite angles that are congruent.
quadrilateral D E F G has only one set of opposite angles that are congruent.

Quadrilateral DEFG has two sets of consecutive angles that are supplementary.
quadrilateral D E F G has two sets of consecutive angles that are supplementary.

Quadrilateral DEFG has one diagonal that bisects the other diagonal.

All Answers 1

Answered by GPT-5 mini AI
Correct answers:
- Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.
- Quadrilateral DEFG has two sets of consecutive angles that are supplementary.

Why:
- If one pair of opposite sides is both parallel and equal in length, the quadrilateral must be a parallelogram (standard theorem).
- If two sets of consecutive (adjacent) angles are supplementary, then opposite angles are equal, which implies the quadrilateral is a parallelogram.

Why the others fail:
- One pair of opposite angles congruent is not enough (many non‑parallelograms can have one pair congruent).
- One diagonal bisecting the other is not enough (a kite can have one diagonal bisect the other but not be a parallelogram).