# Write a two-column proof to show RSTW is a parallelogram using the method that states that if one pair of oppo?

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- Pere DLv 59 years agoFavorite Answer
The goal is to prove that one pair of opposite sides is both parallel and congruent (it having been previously declared and established that this will prove the shape is a parallelogram.)

1. ∠WRS ≅ ∠STW, ∠RSW ≅ ∠TWS | Given.

2. lineSW ≅ lineSW | Reflexive Property.

3. ΔWRS ≅ ΔSTW | AAS: Two angles and a side adjacent congruent to those of a second triangle define the second triangle as congruent to the first.

4. lineRS ║ lineTW | ∠WRS and ∠STW are congruent and alternate interior angles to transversal, lineSW.

5. lineRS ≅ lineTW | All parts of congruent triangles are congruent (and equal in measure, i.e. by length, lineRS = lineTW.)

4 and 5 are QED.

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