Prove that quadrilateral ABCD is a parallelogram. How do you know that the figure is a parallelogram?

(1 point)
Responses

Adjacent sides of the figure are parallel.
Adjacent sides of the figure are parallel.

Opposite sides of the figure are congruent.
Opposite sides of the figure are congruent.

Adjacent sides of the figure are congruent.
Adjacent sides of the figure are congruent.

Adjacent angles of the figure are congruent.

1 answer

To prove that quadrilateral ABCD is a parallelogram, we can rely on specific properties of parallelograms. One valid way to prove this is by demonstrating that opposite sides are congruent.

If you establish that:

  • Opposite sides of the figure are congruent (i.e., \(AB \cong CD\) and \(AD \cong BC\))

Then you can conclude that quadrilateral ABCD is a parallelogram based on the property that states if both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.

Therefore, the correct response is:

Opposite sides of the figure are congruent.

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