Q. 6

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

Answer :


Let ABCD is a parallelogram and diagonal AC bisect A.


CAB = CAD


Now,


AB||CD and AC is a transversal.


CAB = ACD


Again, AD||BC and AC is a transversal.


DAC = ACB


Now,


A = C


A = C


DAC = DCA


AD = CD


But, AB = CD and AD = BC (Opposite sides of parallelograms)


AB = BC = CD = AD


Thus, ABCD is a rhombus.


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