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):
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):

Solution:-

(i) From the ΔABC and ΔPQR

AB/PQ = 3.2/4

= 32/40

Divide both numerator and denominator by 8 we get,

= 4/5

AC/PR = 3.6/4.5

= 36/45

Divide both numerator and denominator by 9 we get,

= 4/5

BC/QR = 3/5.4

= 30/54

Divide both numerator and denominator by 6 we get,

= 5/9

By comparing all the results, the side are not equal.

Therefore, the triangles are not equal.

(ii) From the ΔDEF and ΔLMN

∠E = ∠N = 40o

Then, DE/LN = 4/2

Divide both numerator and denominator by 2 we get,

= 2

EF/MN = 4.8/2.4

= 48/24

Divide both numerator and denominator by 24 we get,

= 2

Therefore, ΔDEF ~ ΔLMN