Question

What property of parallelograms allows us to apply the consecutive interior angles theorem to ∠A and ∠B?
A: opposite angles are congruent.
B: Opposite sides are equal in length.
C: Consecutive angles are supplementary.
D: Opposite sides are parallel.

Answer 1

The property of parallelograms that allows us to apply the consecutive interior angles theorem to angles \(\angle A\) and \(\angle B\) is:

**C: Consecutive angles are supplementary.**

In a parallelogram, consecutive angles are supplementary, which means they add up to \(180^\circ\). This is relevant to the consecutive interior angles theorem, which states that if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. In a parallelogram, the property of consecutive angles being supplementary allows us to apply this theorem because the opposite sides of a parallelogram are parallel.