Question

Draw any $\Delta ABC$. Construct $\Delta DEF$ so that $\Delta DEF~\Delta ABC$ and $DE=2AB$.

Short answer

The required figure is,

Step-by-step solution

Step 1. Given information.

Consider that $\Delta ABC$ be the triangle as shown in below figure,

Step 2. Follow the ways.

Now, to construct $\Delta DEF$ follow the following ways,

Draw a line segment $DE$of $4cm$.

With $D$as center and radius more than half draw arc on side of $DE$.

With $E$as center and same radius as in line $2$.

Draw arc cutting the previous arc at $F$.

Join point $F$so that $DF$ is $2cm$ and $EF$ is $2cm$.

Step 3. Construct the figure.

Consider the fact that $DE=2AB=4cm$

Therefore, by Side angle side property one can say that two triangles are similar.