Chapter 8.3, Problem 11PSA

To determine

To prove : $A\text{'}C\text{'}$ is not equal to $12.3$ .

Explanation of Solution

Given information : Here, we have given that two triangles: $\Delta ABC$ and $\Delta A\text{'}B\text{'}C\text{'}$ .

Proof:

As, $\Delta ABC$ is not a dilation of $\Delta A\text{'}B\text{'}C\text{'}$ ,

  $\begin{array}{l}\Rightarrow \frac{AB}{A\text{'}B\text{'}}\ne \frac{AC}{A\text{'}C\text{'}}\\ \Rightarrow \frac{2}{6}\ne \frac{4.1}{A\text{'}C\text{'}}\\ \Rightarrow \frac{1}{3}\ne \frac{4.1}{A\text{'}C\text{'}}\\ \Rightarrow A\text{'}C\text{'}\ne 12.3\end{array}$