Question

given: abcd is a parallelogram. prove: ∠a and ∠d are supplementary. by the definition of a parallelogram, (overline{ab}paralleloverline{dc}). (overline{ad}) is a transversal between these sides, so ∠a and ∠d are angles. because (overline{ab}) and (overline{dc}) are, the same - side interior angles must be by the same - side interior angles the a and ∠d are supplementary. complementary congruent corresponding supplementary

Explanation:

Step1: Identify angle - type

Since $\overline{AB}\parallel\overline{DC}$ and $\overline{AD}$ is a transversal, $\angle A$ and $\angle D$ are same - side interior angles.

Step2: Apply angle - relationship theorem

By the same - side interior angles theorem, when two parallel lines are cut by a transversal, same - side interior angles are supplementary.

Answer:

$\angle A$ and $\angle D$ are supplementary because they are same - side interior angles formed by parallel lines $\overline{AB}$ and $\overline{DC}$ with transversal $\overline{AD}$, and same - side interior angles are supplementary.