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 { a b } \parallel \overline { d c } \\). \\( \overline { a d } \\) 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:

When two parallel lines (\(\overline{AB}\) and \(\overline{DC}\)) are cut by a transversal (\(\overline{AD}\)), the angles formed on the same side of the transversal (in this case, \(\angle A\) and \(\angle D\)) are called same - side interior angles. According to the same - side interior angles theorem, if two parallel lines are cut by a transversal, then the same - side interior angles are supplementary.

Answer:

Same - side interior; parallel; supplementary