Question

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

Explanation:

Step1: Identify angle type

∠A and ∠D are same - side interior angles (formed by transversal \( \overline{AD} \) with parallel lines \( \overline{AB} \) and \( \overline{DC} \)).

Step2: Recall parallel lines property

\( \overline{AB} \parallel \overline{DC} \) (by definition of parallelogram).

Step3: Apply same - side interior angles theorem

Same - side interior angles are supplementary when lines are parallel. So ∠A and ∠D are supplementary.

Answer:

First blank: same - side interior; Second blank: parallel; Third blank: supplementary