Similar Triangles (moved)

[rachelmaddie]

I’m stuck with this as well

 

[Harry_the_cat]

I’m having trouble setting up the proportion. How did get those lengths in the picture?

Draw triangles ADE and ACB separately. Now mark in the angles that ate equal and all of the sides you know.

 

[Harry_the_cat]

$\displaystyle \frac{BC}{GH}=\frac{8}{12} =\frac{2}{3}$
$\displaystyle \frac{AC}{FH}=\frac{10}{15} =\frac{2}{3}$
But:
$\displaystyle \frac{AB}{FG} = 1$ since AB = FG (shown on the diagram)

For the triangles to be similar, the proportions of all 3 pairs of sides has to be the same.
Here they aren't, so the triangles are not similar.

 

[rachelmaddie]

$\displaystyle \frac{BC}{GH}=\frac{8}{12} =\frac{2}{3}$
$\displaystyle \frac{AC}{FH}=\frac{10}{15} =\frac{2}{3}$
But:
$\displaystyle \frac{AB}{FG} = 1$ since AB = FG (shown on the diagram)

For the triangles to be similar, the proportions of all 3 pairs of sides has to be the same.
Here they aren't, so the triangles are not similar.

Okay I understand that. AB: FG do not have the same ratio. Thank you!