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.
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