Given: abcd is a parallelogram. prove: any two consecutive angles of abcd are supplementary. the quadrilateral abcd is a parallelogram, so by definition ab¯∥cd¯. it follows that ad¯ is a transversal of parallel line segments ab¯ and cd¯, which makes ∠a and ∠d same-side interior angles along parallel line segments. likewise, bc¯ is a transversal of parallel line segments ab¯ and cd¯, so ∠b and ∠ are same-side interior angles along parallel line segments therefore, applying the same-side interior angles theorem, it is possible to conclude that ∠a is to ∠d and ∠b is to ∠ using the same line of reasoning, but instead consider that ad¯ is parallel to segment and these parallel lines are cut by transversals cd¯ and ab¯. therefore, it is possible to conclude that ∠a is to ∠b and ∠c is supplementary to ∠d. enter the words or names that correctly fill in the blanks to complete the proof. make sure your answers are in order and separate them with commas, like this: x, opposite, xy c, a same-side interior angle , bc