Chapter 11.8, Problem 6IP

To determine

To find: Determine if the two figures are similar by using transformations.

Answer to Problem 6IP

Both rectangles are Not similar.

Explanation of Solution

From Given figure

We get

From Rectangle $ABCD$

  $\begin{array}{l}AB=4\\ BC=6\\ CD=4\\ DA=6\end{array}$

From $\Delta EFHG$

  $\begin{array}{l}EF=2\\ FH=5\\ HG=2\\ GE=5\end{array}$

If two polygons are similar then the ratio of the lengths of the two corresponding sides is the scale factor.

Ratio of lengths of each side are

  $\begin{array}{l}\frac{EF}{AB}=\frac{2}{4}\\ \Rightarrow \frac{EF}{AB}=\frac{1}{2}\end{array}$

  $\frac{FH}{BC}=\frac{5}{6}$

  $\begin{array}{l}\frac{GH}{CD}=\frac{2}{4}\\ \Rightarrow \frac{GH}{CD}=\frac{1}{2}\end{array}$

  $\begin{array}{l}\frac{GE}{DA}=\frac{2}{4}\\ \Rightarrow \frac{GE}{DA}=\frac{5}{6}\end{array}$

As ratios are Not equal so, bothrectangles are not similar.

So,

Both rectangles are Not similar.