Question

Select the correct answer from each drop-down menu. Given: Quadrilateral is a parallelogram with side extended to point E. Prove: is supplementary to . Complete the proof to show that consecutive angles of parallelograms are supplementary.

1) Quadrilateral is a parallelogram.
2) and are a linear pair.
3) is supplementary to .
4) Definition of supplementary
5) Definition of parallelogram

Answer 1

To prove that consecutive angles of parallelograms are supplementary, one uses properties of a parallelogram and the definition of supplementary angles to show that the angles add up to 180 degrees.

Step-by-step explanation:

The student is asked to complete a geometric proof that shows consecutive angles of parallelograms are supplementary. A parallelogram has opposite sides that are parallel and equal in length, and its consecutive angles are supplementary, meaning they add up to 180 degrees. When a side of a parallelogram is extended to a point E, the adjacent angles form a linear pair, which by definition are also supplementary.

The proof would proceed with a series of logical steps based on definitions and theorems:

1. Quadrilateral is a parallelogram (Given).
2. Adjacent angles ∠A and ∠E are a linear pair (Given).
3. Angles ∠A is supplementary to ∠E (Definition of a linear pair).
4. Because ∠A and ∠E are supplementary, their measures add up to 180 degrees (Definition of supplementary).
5. The definition of a parallelogram indicates that consecutive angles are supplementary (Definition of parallelogram).

Therefore, it follows that in a parallelogram, since consecutive angles ∠A and ∠E form a linear pair, and are additive to 180 degrees, these angles are indeed supplementary.