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 D
    Lv 5
    9 years ago
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    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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