To prove that quadrilateral ABCD is a parallelogram, we can rely on several properties that characterize parallelograms. Based on the responses you provided, here are the two options that would serve as valid proofs:
-
Opposite sides of the figure are congruent: If we can show that the lengths of opposite sides are equal, i.e., \(AB = CD\) and \(BC = AD\), then by the properties of parallelograms, we can conclude that quadrilateral ABCD is a parallelogram.
-
Adjacent angles of the figure are congruent: If we can demonstrate that the measures of adjacent angles are equal, for example, \( \angle A = \angle B\) and \( \angle B = \angle C\), then ABCD would also qualify as a parallelogram by the properties of angles in a parallelogram.
Among the options you listed, the most straightforward way to demonstrate that ABCD is a parallelogram is by showing that opposite sides of the figure are congruent.
3 answers