Chapter 11.8, Problem 7IP

To determine

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

Answer to Problem 7IP

Both rectangles are Not similar.

Explanation of Solution

From Given figure

We get

From Rectangle $CDEF$

  $\begin{array}{l}CD=6\\ DE=2\\ EF=6\\ FC=2\end{array}$

From Rectangle $GHIJ$

  $\begin{array}{l}GH=4\\ HI=1\\ IJ=4\\ JG=1\end{array}$

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

  $\begin{array}{l}\frac{GH}{CD}=\frac{4}{6}\\ \Rightarrow \frac{GH}{CD}=\frac{2}{3}\end{array}$

  $\frac{HI}{DE}=\frac{1}{2}$

  $\begin{array}{l}\frac{IJ}{EF}=\frac{4}{6}\\ \Rightarrow \frac{IJ}{EF}=\frac{2}{3}\end{array}$

  $\frac{JG}{FC}=\frac{1}{2}$

As ratios are Not equal so, both rectangles are not similar.

So,

Both rectangles are Not similar.