Chapter 8.3, Problem 8PSA

To determine

To find : Whether $\Delta FGH$ is similar to $\Delta F\text{'}G\text{'}H\text{'}$ or not

Explanation of Solution

Given information : Here, we have given that $FG=6$ , $GH=8$ , $FH=12$ , $F\text{'}G\text{'}=15$ , $G\text{'}H\text{'}=20$ and $F\text{'}H\text{'}=30$ .

  

Proof: If the ratio of corresponding sides of two triangles is equal, then the two triangles are said to be similar.

Now,

  $\frac{FG}{F\text{'}G\text{'}}=\frac{6}{15}=\frac{2}{5}$

Similarly, $\frac{GH}{G\text{'}H\text{'}}=\frac{8}{20}=\frac{2}{5}$

And, $\frac{FH}{F\text{'}H\text{'}}=\frac{12}{30}=\frac{2}{5}$

As, $\frac{FG}{F\text{'}G\text{'}}=\frac{GH}{G\text{'}H\text{'}}=\frac{FH}{F\text{'}H\text{'}}$

  $\Rightarrow \Delta FGH$ is similar to $\Delta F\text{'}G\text{'}H\text{'}$ (as, ratio of corresponding sides is equal)

  $\therefore \Delta FGH\sim \Delta F\text{'}G\text{'}H\text{'}$