ABCD is a parallelogram.The circle through A,B and C intersect CD (produce if necessary) at E.Prove that AE = AD. -Maths 9th

ABCD is a parallelogram.The circle through A,B and C intersect CD (produce if necessary) at E.Prove that AE = AD. -Maths 9th
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Solution  :- ∠ABC + ∠AEC = 1800  (Opposite angles of cyclic quadrilateral)  .. . (i) ∠ADE + ∠ADC = 1800 (Linear pair) But         ∠ADC = ∠ABC (Opposite angles of ||gm) ∴ ∠ADE + ∠ABC = 1800  .. (ii) From equations (i) and (ii),we have     ∠ABC + ∠AEC = ∠ADE + ∠ABC  ⇒     ∠AEC = ∠ADE  ⇒   AD = AE (sides opposite to equal angles)
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