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.

AD is a transversal between these sides, so ∠A and ∠D are supplementary angles.

Step-by-step explanation:

Supplementary angles are two or more angles that sum up to . And a parallelogram has opposite side to be parallel and equal. With the sum of interior angles to be .

Given that: AB∥DC

<A and <D are consecutive angles of the parallelogram.

AD is the transversal of the interior angles A and D, so that the addition of <A and <D gives the sum of angles on a straight line.

Therefore, AD is a transversal between these sides, so ∠A and ∠D are supplementary angles.