How Dow you that the opposite angles of a parallelogram are equal?

Answer 1

First of all, you know the opposite sides of a parallelogram are equal because of the definition of a parallelogram. Therefore, two adjacent angles in the parallelogram are supplementary, because same-side interior angles in two parallels and a transversal are always supplementary. Therefore, opposite angles in a paralellogram are equal, because two angles both supplementary to a third angle are equal to each other.