Q6 of 56 Page 82

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


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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