State which pairs of triangles in the figure given below are similar. Write the similarity rule used and also write the pairs of similar triangles in symbolic form (all lengths of sides are in cm):

Given,

(i) In △ABC and △PQR

$\dfrac{AB}{PQ} = \dfrac{3.2}{4} \\[1em] = \dfrac{32}{40} = \dfrac{4}{5} \\[1em] \dfrac{AC}{PR} = \dfrac{3.6}{4.5} \\[1em] = \dfrac{36}{45} = \dfrac{4}{5} \\[1em] \dfrac{BC}{QR} = \dfrac{3}{5.4} \\[1em] = \dfrac{30}{54} = \dfrac{5}{9}$

Since, the ratio of the sides of both the triangle are not same. Hence, they are not similar.

(ii) In △DEF and △LMN

∠ E = ∠ N = 40°

$\dfrac{DE}{LN} = \dfrac{4}{2} = \dfrac{2}{1} \\[1em] \dfrac{EF}{MN} = \dfrac{4.8}{2.4} = \dfrac{2}{1} \\[1em]$

Thus, by SAS rule of similarity △DEF ~ △LMN.