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Hello Anshika,
Given,
ABCD is a parallelogram.
So, AB is parallel to DC.
So,
∠EAB = ∠DEA (Alternating angles)
∴ ∠DAE = ∠ DEA
∴ ADE is an isosceles Δ
AD = AE
Similarly,
EC =CB
DE + EC = AB (Opposite sides of a parallelogram are equal)
Substituting the values from earlier expressions,
AD + CB = AB
⇒ 2BC = AB (BC = AD because the opposite sides of a parallelogram are equal.)
⇒ AB = 2BC
Hence, proved.
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anshikakumari20:
thanks
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