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 \\(\angle a\\) and \\(\angle d\\) are \\(\underline{\quad\quad\quad\quad\quad\quad}\\) angles. because \\(\overline{ab}\\) and \\(\overline{dc}\\) are \\(\underline{\quad\quad\quad\quad\quad\quad}\\), the same - side interior angles must be \\(\underline{\quad\quad\quad\quad\quad\quad}\\) by the same - side interior angles theorem. therefore, \\(\angle a\\) and \\(\angle d\\) are supplementary.

Explanation:

Step1: Identify angle type

When a transversal (AD) intersects two parallel lines (AB || DC), ∠A and ∠D are same - side interior angles.

Step2: Recall parallel line property

AB and DC are parallel (given by the definition of a parallelogram).

Step3: Apply same - side interior angles theorem

By the same - side interior angles theorem, same - side interior angles are supplementary when the lines are parallel.

Answer:

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