Given: AM = 6cm and DN = 9cm
Here, ΔABC and ΔDEF are similar triangles
We know that, in similar triangles, corresponding angles are in the same ratio.
⇒∠A = ∠D, ∠B = ∠E and ∠C = ∠F ……(i)
In △ABM and △DEN
∠B = ∠E [from (i)]
and ∠M = ∠N [each 90°]
∴ △ABC ~ △DEF [by AA similarity]
So, AM/DN = AB/DE = BM/EN ……(ii)
We know that, the ratio of two similar triangles is equal to the square of the ratio of their corresponding sides.