Only 20 percent of the spectators left the contest discontented. If 6000 spectators left the contest contented, how many left discontented?

answer: the missing part will ab and cd are congruent by sas postulate.

explanation: according to the question here, a quadrilateral abcd in which o is the point at which the diagonals ac and bd cut each other. and, and are the angles of triangles aob and cod respectively.

now the theorem is " if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram"

so, according to melissa's proof- for triangles aob and cod, angle 1 is equal to angle 2 as they are vertical angles.

ao = oc and bo = od because it is given that diagonals bisect each other.

the ab and cd are congruent by sas postulates.

similarly, triangles aod and cob are congruent.  

by cpctc, ab is equal to dc.  

by cpctc, ad is equal to bc.  

as the opposite sides are congruent the quadrilateral abcd is a parallelogram.