Question

In the parallelogram $ABCD$, the dissectors of $\angle A$ and $\angle B$ meet $CD$ at the point $E$. The length of the side $BC$ is $2cm$. Find the length of the side $AB$ ?

Answer 1

ABCD is a parallelogram. BC = 2. Bisectors of <A and <B meet CD at E. We want the length of AB.

Let <A = 2x and <B = 2y.

So ∆ABE is a right angled triangle, with <BAE = x and <ABE = y and <AEB = 90 deg,

In ∆ADE, <DAE = <AED =x, <ADE = 2y, AD = 2. So ∆ADE is an isosceles triangle and DE=DA = 2.

In ∆BCE, <BCE = 2x, <EBC=<BEC = y, AD = 2. So BCE is an isosceles triangle and CE=CB = 2.

Hence CD = CE+ED = 2+2 = 4.

So AB=CD = 4 and BC=AD = 2