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Trapezoid Proof (Posted on 2008-04-17) Difficulty: 3 of 5
Two opposite sides of a quadrilateral are the same length. The diagonals of the quadrilateral are also the same length. Prove the quadrilateral is a trapezoid.

No Solution Yet Submitted by Brian Smith    
Rating: 2.5000 (2 votes)

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Solution Solution | Comment 1 of 4

Let ABCD be the quadrilateral with
|AB| = |CD| and |AC| = |BD|.
Triangles ABC and DCB are congruent by SSS
  ==> angle ABC = angle DCB = angle BCD
Triangles BAD and CDA are congruent by SSS
  ==> angle CDA = angle BAD = angle DAB
360 = angle ABC + angle BCD +
      angle CDA + angle DAB
    = 2(angle ABC) + 2(angle DAB)
180 = angle ABC + angle DAB
  ==> DA || BC
  ==> ABCD is a trapezoid.

  Posted by Bractals on 2008-04-17 13:01:22
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