Question
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 angles of the figure are congruent. Adjacent angles of the figure are congruent. Adjacent sides of the figure are congruent.
Answers
GPT-4o mini
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:
1. **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.
2. **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**.
1. **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.
2. **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**.