Question

Prove that if 2 non parallel sides of a trapezium are equal , then it is cyclic​

Answer 1

 we have taken a trap in ABCD are sides of trapezium.. construction: draw perp from angle A and Angle B on side DC..

 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 ....

Answer 2

Hello I hope it's help u