# Write a proof to show triangles ABC and DEF are similar. \triangle ABC with AB=4, BC=6 and CA = 2 \triangle DEF with DE=2, EF=3 and FD = 1

Write an informal proof to show triangles ABC and DEF are similar.

Given,
$$\displaystyle\triangle{A}{B}{C}$$ with AB=4, BC=6 and CA = 2
$$\displaystyle\triangle{D}{E}{F}$$ with DE=2, EF=3 and FD = 1
We have to prove the two triangles are similar.

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sovienesY
In $$\displaystyle\triangle{A}{B}{C}\ {\quad\text{and}\quad}\ \triangle{D}{E}{F}$$
Taking the ratio of sides
$$\displaystyle\Rightarrow{\frac{{{A}{B}}}{{{D}{E}}}}={\frac{{{B}{C}}}{{{E}{F}}}}={\frac{{{C}{A}}}{{{F}{D}}}}$$
$$\displaystyle\Rightarrow{\frac{{{4}}}{{{2}}}}={\frac{{{6}}}{{{3}}}}={\frac{{{2}}}{{{1}}}}={2}$$
So,
The ratio of corresponding sides are equal,
Then, from SSS(side-side-side) rule of similarity
$$\displaystyle\triangle{A}{B}{C}\sim\triangle{D}{E}{F}$$