Question

hi i m jiya had a dout

Answer 1

In ΔAED and ΔBFC, AD = BC     (Given) DE = CF    (Distance between parallel sides is same)∠AED = ∠BFC = 90° ΔAED ≅ ΔBFC  (RHS Congruence criterion) 
Hence ∠DAE = ∠CBF  (CPCT)  … (1) Since AB||CD, AD is transversal ∠DAE + ∠ADC = 180°  (Sum of adjacent interior angles is supplementary) ⇒ ∠CBF + ∠ADC = 180°  [from (1)]Since sum of opposite angles is supplementary in trapezium ABCD.Thus ABCD is a cyclic trapezium