Chapter 11.8, Problem 1GP

To determine

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

Answer to Problem 1GP

Given two rectangles are not similar.

Explanation of Solution

From Given figure

We get

From rectangle $ABCD$

  $\begin{array}{l}AB=5\\ BC=2\\ CD=5\\ AD=2\end{array}$

From rectangle $EFGH$

  $\begin{array}{l}EF=7\\ FG=3\\ GH=7\\ HE=3\end{array}$

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

  $\begin{array}{l}\frac{AB}{EF}=\frac{5}{7}\\ \frac{BC}{FG}=\frac{2}{3}\\ \frac{CD}{GH}=\frac{5}{7}\\ \frac{AD}{HE}=\frac{2}{3}\end{array}$

On comparing we can say ratios are not equal

So, given two rectangles are not similar.