Question

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

Answer 1

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 $\angle c$

[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.

Answer 2

the answers are D, SUPPLEMENTARY, BC and D