Given: ABCD is a parallelogram. Prove: ∠A and ∠D are supplementary.

Parallelogram A B C D is shown.

By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are
angles. Because AB and DC are
, the same-side interior angles must be
by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.