State which of the following pairs of triangles are similar. Write the similarity criterion used and write the pairs of similar triangles in symbolic form (all lengths of sides are in cm).

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(i) In ABC,

∠A = 70° and ∠B = 50°

And we know that, sum of the angles = 180°

⇒∠A + ∠B +∠C = 180°

⇒70° + 50° +∠C = 180°

⇒ 120° +∠C = 180°

⇒ ∠C = 60°

And In DEF

∠F = 70° and ∠E = 50°

And we know that, sum of the angles = 180°

⇒∠D + ∠E +∠F = 180°

⇒∠D + 50° + 70° = 180°

⇒ ∠D = 60°

Yes,ABC ~ DEF [by AAA similarity criterion]

(ii) In ABC and PQR

Here,

As,

So, ABC ~ PQR [by SSS similarity criterion]

(iii) InMNL and PQR

∠NML = ∠PQR = 70°

and

No, the two triangles are not similar.

(iv) InPQR and LMN

∠PQR = ∠LNM = 50°

and

∴PQR ~ LMN [by SAS similarity criterion]

(v) In LMP and DEF

Here,

As

So, no two triangles are not similar

(vi) In ABC and PQR

∠A = ∠Q = 85°

∠B = ∠P = 60°

and ∠C =∠R = 35°

So, PQR ~ LMN [by AAA similarity]

(vii) In ABC and PQR

Here,

As,

So, ABC ~ PQR [by SSS similarity criterion]