Which triangles are similar to triangle ABC?
The sides of similar triangles are always proportional. This is known as
\color{orange}{Side-Side-Side (SSS) Similarity}.
First, let's determine whether ABC and DEF are similar.
In triangle DEF, DE = DEF_SIDES[2], EF = DEF_SIDES[0], and FD = DEF_SIDES[1].
In triangle ABC, AB = ABC_SIDES[2], BC = ABC_SIDES[0], and CA = ABC_SIDES[1].
In order for ABC and DEF to be similar:
\dfrac{AB}{\color{blue}{DE}} = \dfrac{BC}{\color{blue}{EF}} = \dfrac{CA}{\color{blue}{FD}}
Substitute in the proper values for each side.
\dfrac{ABC_SIDES[2]}{\color{blue}{DEF_SIDES[2]}} DEF_COMP_1 \dfrac{ABC_SIDES[0]}{\color{blue}{DEF_SIDES[0]}} DEF_COMP_2 \dfrac{ABC_SIDES[1]}{\color{blue}{DEF_SIDES[1]}}
Since not all the proportions are equal, ABC is not similar to DEF.
Since all the proportions are equal, ABC is similar to DEF.
Next, let's determine whether ABC and GHI are similar.
In triangle GHI, GH = GHI_SIDES[2], HI = GHI_SIDES[0], and IG = GHI_SIDES[1].
In triangle ABC, AB = ABC_SIDES[2], BC = ABC_SIDES[0], and CA = ABC_SIDES[1].
For triangles ABC and GHI to be similar:
\dfrac{AB}{\color{red}{GH}} = \dfrac{BC}{\color{red}{HI}} = \dfrac{CA}{\color{red}{IG}}
Substitute in the proper values for each side.
\dfrac{ABC_SIDES[2]}{\color{red}{GHI_SIDES[2]}} GHI_COMP_1 \dfrac{ABC_SIDES[0]}{\color{red}{GHI_SIDES[0]}} GHI_COMP_2 \dfrac{ABC_SIDES[1]}{\color{red}{GHI_SIDES[1]}}
Since not all the proportions are equal, ABC is not similar to GHI.
Since all the proportions are equal, ABC is similar to GHI.
DEF is similar to ABC
GHI is similar to ABC
DEF and GHI are similar to ABC
Neither DEF nor GHI are similar to ABC