Question

why or why not does this quad represent a parallelogram?

Answer 1

It is a parallelogram. This is justified by the fact that, if alternate interior angles are congruent, the two lines cut by the transversal are parallel. This can be used to show that opposite sides of the figure are parallel.

Answer 2

does it not have to show that both sets of opposite angles are congruent-not just one set of opposite angles as shown in my diagram

Answer 3

If it just showed that one pair of opposite angles are congruent, you'd be right. That wouldn't be enough to determine whether it's a parallelogram. But it provides a diagonal, and states that alternate interior angles on the diagonal are congruent. This gives more information, and is in fact enough to determine that the figure is a parallelogram.

Answer 4

are u saying there is only one set of parallel lines in this so called parallelogram?