Question

In the given figure, ABCD is a parallelogram.

Prove that: AB = 2 BC.

Answer 1

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.