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Question
In the given figure, ABCD is a parallelogram.
Prove that: AB = 2 BC.
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Solution
Given ABCD is a parallelogram
To prove: AB = 2BC
Proof: ABCD is a parallelogram
A + D + B + C = 180°
From the AEB we have
⇒ `("∠A")/(2) + ("∠B")/(2)` + E = 180°
⇒ ∠A - `("∠A")/(2)` + ∠D + ∠E1 = 180° ...[taking E1 as new angle]
⇒ ∠A + ∠D + ∠E1 = 180° + `("∠A")/(2)`
⇒ ∠E1 = `("∠A")/(2)` ...[Since ∠A + ∠D = 180°]
Again,
similarly,
∠E1 = `("∠B")/(2)`
Now
AB = DE + EC
= AD + BC
= BC + BC
= 2BC ...[since AD = BC]
Hence, proved.
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