Chapter 11.8, Problem 8IP

To determine

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

Answer to Problem 8IP

The two triangles are similar because a translation and Dilation maps $\Delta LNM$ on to $\Delta PRQ$

Explanation of Solution

From Given figure

We get

From Triangle $LMN$

  $\begin{array}{l}LM=3.6\\ MN=3\\ NL=2\end{array}$

From Rectangle $PQR$

  $\begin{array}{l}PQ=7.2\\ QR=6\\ RP=4\end{array}$

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

  $\begin{array}{l}\frac{PQ}{LM}=\frac{7.2}{3.6}\\ \Rightarrow \frac{PQ}{LM}=2\end{array}$

  $\begin{array}{l}\frac{QR}{MN}=\frac{6}{3}\\ \Rightarrow \frac{QR}{MN}=2\end{array}$

  $\begin{array}{l}\frac{RP}{NL}=\frac{4}{2}\\ \Rightarrow \frac{RP}{NL}=2\end{array}$

As ratios are equal So, both rectangles are not similar.

  $\Delta PRQ$ is a Dilated image of $\Delta LNM$ .

Here translation also occurs

Translate $\Delta LNM$ $6$ units down and $1$ unit right So, $N$ maps onto $R$

So, the two triangles are similar because a translation and Dilation maps $\Delta LNM$ on to $\Delta PRQ$