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If the non-parallel sides of a trapezium are equal, prove that it is cyclic. |
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Answer» InΔAED andΔBFC,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 |
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