State which pairs of triangles in Fig. 6.34 are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :

(i) In ΔABC and ΔPQR

∠A = ∠P = 60

∠B = ∠Q = 80

∠C = ∠R = 40

All the corresponding angles of the triangles are equal.

By AAA criterion ΔABC ∼ ΔPQR

(ii)In ΔABC and ΔQRP

AB/QR = 2/4 = 1/2

BC/PR = 2.5/5 = 1/2

AC/PQ = 3/6 = 1/2

⇒ AB/QR = BC/PR = AC/PQ = 1/2

All the corresponding sides of the two triangles are in the same proportion. By SSS criterion ΔABC ∼ ΔQPR.

(iii) In ΔLMP and ΔFED

LM/FE = 2.7/5

MPED = 2/4 = 1/2

LP/FD = 3/6 = 1/2

⇒ LM/FE ≠ MP = LP/FD

All the corresponding sides of the two triangles are not in the same proportion. Hence triangles are not similar. ΔLMP ∼ ΔFED.

(iv) In ΔNML and ΔPQR

NM/PQ = 2.5/5 = 1/2

M/QR = 5/10 = 1/2

⇒ NM/PQ = ML/QR = 1/2

∠M = ∠Q = 70°

One angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional.

By SAS criterion ⇒ ΔNML ∼ ΔPQR

(v) In ΔABC and ΔDFE

AB/DF = 2.5/5 = 1/2

BC/EF = 3/6 = 1/2

AB/DF = BC/EF = 1/2

∠A = ∠F = 80

But ∠B must be equal to 80°

The sides AB, BC includes ∠B , not ∠A)

Therefore, SAS criterion is not satisfied

Hence, the triangles are not similar, ΔABC ∼ ΔDFE.

(vi) In ΔDEF

∠D = 70°, ∠E = 80°

⇒ ∠F = 30° [∵ Sum of the angles in a triangle is 180°]

Similarly,

In ΔPQR

∠Q = 80° , ∠R = 30°

⇒ ∠P = 70°

In ΔDEF and ΔPQR

∠D = ∠P = 70°

∠E = ∠Q = 80°

∠F = ∠R = 30°

All the corresponding angles of the triangles are equal.

By AAA criterion ΔDEF ∼ ΔPQR.