Question

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

Explanation:

Step1: Identify the type of angles

Since \(AD\) is a transversal between \(AB\parallel DC\), \(\angle A\) and \(\angle D\) are same - side interior angles.

Step2: Use the property of parallel lines

Because \(AB\) and \(DC\) are parallel (\(AB\parallel DC\)), by the same - side interior angles theorem, same - side interior angles are supplementary.

Answer:

Same - side interior; parallel; supplementary