Question

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Answer 1

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In ΔAED and ΔBFC,

AD = BC     {Given}

DE = CF     {Distance Between the Parallel Sides}

∠AED = ∠BFC = 90°

ΔAED is congruent to ΔBFC    { RHS Congruency Criteria}

Hence,

∠DAE = ∠CBF  (CPCT) .... (1)

Since

AB || CD,

AD is transversal.

∠DAE + ∠ADC = 180°

{Sum of adjacent interior angles is 180°}

⇒ ∠CBF + ∠ADC = 180°   [From 1.]

Since the sum of opposite angles is supplementary, the trapezium is a cyclic quadrilateral.

Hence Proved.

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