Question

In the given figure, ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ∼ ∆ADE and hence find the length of AE and DE.

Answer 1

It is given that is right angle triangle and

We have to prove that and find the lengths of and .

In ∆ABC ∼ ∆ADE,

$$\begin{gathered} \angle A=\angle A\left(\mathrm{Common}\right) \\ \angle C=\angle E\left(90°\right) \end{gathered}$$

So by similarly criterion, we have

Since

So

And

Hence, and