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Question:

State which pairs of triangles in Fig. 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.

Solution:

(i) In ΔABC and ΔPQR ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R, ∴ By AAA criterion of similarity, ΔABC ≅ ΔPQR
(ii) In ΔABC and ΔQRP AB/QR = BC/RP = AC/QP = 1/2 ∴ By SSS criterion of similarity, ΔABC ≅ ΔQRP
(iii) In ΔLMP and ΔDEF LM/DE = 2.74, LP/DF = 1/2 The sides are not in the equal ratios, Hence the two triangles are not similar
(iv) In ΔMNL and ΔQPR ∠M = ∠Q, MN/QP = ML/QR = 1/2 ∴ By SAS criterion of similarity, ΔMNL ≅ ΔQPR
(v) In ΔABC and ΔEFD ∠A = ∠F, AB/FD = BC/FD = 1/2 ∴ By SAS criterion of similarity, ΔABC ≅ ΔEFD
(vi) In ΔDEF and ΔPQR Since, sum of angles of a triangle is 180o, Hence, ∠F = 30o and ∠P = 70o ∠D = ∠P, ∠E = ∠Q, ∠F = ∠R, ∴ By AAA criterion of similarity, ΔDEF ≅ ΔPQR