Ask a New Question
Menu

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

1 answer

To prove that quadrilateral ABCD is a parallelogram, we can use the property regarding opposite sides. Specifically, if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  1. Identify Congruent Opposite Sides: Suppose sides AB and CD are congruent (AB ≅ CD), and sides BC and AD are also congruent (BC ≅ AD).

  2. Application of the Property: According to the properties of quadrilaterals:

    • If AB ≅ CD and BC ≅ AD, then quadrilateral ABCD is a parallelogram.

Therefore, if we know that opposite sides of figure ABCD are congruent, we can conclude that ABCD is a parallelogram.

Conclusion:

Answer: Opposite sides of the figure are congruent.