Question

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).

Answer 1

(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

No, the two triangles are not similar.

(iv) In △PQR and △LMN

∠PQR = ∠LNM = 50°

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