Question

proving part of the supplementary consecutive angles theorem
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

When a transversal intersects two parallel lines, angles between the lines on the same side of the transversal are same-side interior angles. Here, $\overline{AD}$ is the transversal for $\overline{AB} \parallel \overline{DC}$, so $\angle A$ and $\angle D$ are same-side interior angles.

Step2: Confirm parallel lines

By the given definition of a parallelogram, $\overline{AB} \parallel \overline{DC}$.

Step3: Apply angle theorem

The same-side interior angles theorem states that same-side interior angles formed by a transversal with parallel lines are supplementary (sum to $180^\circ$).

Answer:

1. same-side interior
2. parallel
3. supplementary