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 \\( \angle a \\) and \\( \angle 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, \\( \angle a \\) and \\( \angle d \\) are supplementary.

Explanation:

• When two parallel lines (\(\overline{AB}\) and \(\overline{DC}\)) are cut by a transversal (\(\overline{AD}\)), the angles formed (\(\angle A\) and \(\angle D\)) are same - side interior angles.
• The same - side interior angles theorem states that if two parallel lines are cut by a transversal, then the same - side interior angles are supplementary.

Answer:

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