Question

In the given figure, DE || BC and $\mathrm{AD}=\frac{1}{2}\mathrm{BD}$. If BC = 4.5 cm, find DE.

Answer 1

Given: In ∆ABC, DE || BC. and BC = 4.5 cm.

To find: DE

In ∆ABC and ∆ADE

$$\begin{gathered} \angle \mathrm{B}=\angle \mathrm{ADE}\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle \mathrm{A}=\angle \mathrm{A}\left(\mathrm{Common}\right) \\ \therefore ∆\mathrm{ABC}~∆\mathrm{ADE}\left(\mathrm{AA}\mathrm{Similarity}\right) \end{gathered}$$