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 ∠___[1]____ 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 ___[2]____ to ∠d and ∠b is ___[2]____ to ∠___[1]____. using the same line of reasoning, but instead consider that ad¯ is parallel to segment ___[3]____ and these parallel lines are cut by transversals cd¯ and ab¯. therefore, it is possible to conclude that ∠a is ___[2]____ 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

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For a better understanding of the answer provided here, please have a look at the attached diagram.

The diagram has been made as per the information provided in the question.

From the statements in the question we can see that:

[1] is the angle [tex] \angle c [/tex]

[2] is Supplementary

[3] is the segment bc

Thus, the above are the words or names that correctly fill in the blanks to complete the proof.

Ver imagen Vespertilio

the answers are D, SUPPLEMENTARY, BC and D

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