To prove that quadrilateral ABCD is a parallelogram, we can use one of several properties that confirm a shape is a parallelogram. Here’s a quick overview of some of these properties:
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Opposite sides are parallel: If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.
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Opposite sides are congruent: If both pairs of opposite sides are congruent, the quadrilateral is a parallelogram.
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Opposite angles are congruent: If both pairs of opposite angles are congruent, the quadrilateral is a parallelogram.
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Diagonals bisect each other: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
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One pair of opposite sides is both parallel and congruent: If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram.
Given your options, here’s how we can confirm the proof based on the appropriate property:
- If opposite sides of the figure are congruent, then quadrilateral ABCD is indeed a parallelogram.
So, in response to how you know that the figure is a parallelogram, the correct response would be:
Opposite sides of the figure are congruent.
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