# If the non parallel sides of a trapezium are equal then prove that it is a cyclic......

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by ShaRa11

plz. ..... rply fast. ..plzzz

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by ShaRa11

plz. ..... rply fast. ..plzzz

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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 .

Construction : Draw EB parallel to AD

To Prove : ABCD is cyclic

Proof : ABED is a Parallelogram

∠A = ∠E

ΔBEC is an isosceles triangle

∠DEB + ∠BEC = 180°

∠DEB+∠BCE = 180°

∴∠A + ∠C = 180°