the diagonals of quad. ABCD intersect each other at the point O such that AO/BO=CO/DO . Show that ABCD is a trapezium
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do/bo = co/ao
angle aob = angle doc (V.O.A)
by SAS
triangle aob is similar to triangle cod
hence angle bac = angle acd (alt int angles)
since we know alternate int. lines forms between parrallel lines..
hence
ab||dc
and we know in trapezium two lines of the opposite side are parallel
hence abcd is a trapezium
angle aob = angle doc (V.O.A)
by SAS
triangle aob is similar to triangle cod
hence angle bac = angle acd (alt int angles)
since we know alternate int. lines forms between parrallel lines..
hence
ab||dc
and we know in trapezium two lines of the opposite side are parallel
hence abcd is a trapezium
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