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A parallelogram has its vertices labeled upper A upper B upper C upper D. Two sets of opposite sides are marked as congruent.

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

(1 point)
Responses

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

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

Adjacent angles of the figure are congruent.
Adjacent angles of the figure are congruent.

Adjacent sides of the figure are congruent.

1 answer

To prove that quadrilateral ABCD is a parallelogram, we can use the property of opposite sides being congruent. In a parallelogram, one of the key characteristics is that both pairs of opposite sides are congruent.

Since it is given that two sets of opposite sides are marked as congruent, we have:

  1. AB ≅ CD (one pair of opposite sides).
  2. BC ≅ AD (the other pair of opposite sides).

According to the properties of quadrilaterals, if both pairs of opposite sides are congruent, then the quadrilateral must be a parallelogram.

Therefore, the correct response is:

  • Opposite sides of the figure are congruent.