Question

In figure, $\angle B=\angle D={90}^0$ and $BC=CD$. Is $AB=DE$? Why?

Answer 1

In right angled triangles $ABC$ and $CDE$
$\angle B=\angle D={90}^0$ (given)
$\angle ACB=\angle DCE$ (vertically opposite angles)
and $BC=CD$ (given)
$\Delta ABC=\Delta CDE$ (by ASA congruency property)
$AB=DE$ (by c.p.c.t)
Similarly, Yes, $AB$ and $DE$ are equal.