Chapter 10.1, Problem 21WE

To determine

To construct: $\Delta DEF$ , so that $\Delta DEF\sim \Delta ABC$ and $DE=2AB$ .

Explanation of Solution

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

  

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

Step 1: Draw a line segment $DE$ of 4 cm.

Step 2: With $D$ as center and radius more than half draw arc on side of $DE$ .

Step 3: With $E$ as center and same radius as in step 2.

Draw arc cutting the previous arc at $F$ .

Step 4: Join point $F$ so that $DF$ is 2 cm and $EF$ is 2 cm.

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

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