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# State which pairs of triangles in Figure, 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: Q.1

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What is the best way to solve the all part of this question from triangles of exercise 6.3 of class 10th math, please help me to solve this question State which pairs of triangles in Figure, 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:

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1. (i) Given, in Î”ABC and Î”PQR,

âˆ A = âˆ P = 60Â°

âˆ B = âˆ Q = 80Â°

âˆ C = âˆ R = 40Â°

Therefore by AAA similarity criterion,

âˆ´ Î”ABC ~ Î”PQR

(ii) Given, in Î”ABC and Î”PQR,

AB/QR = BC/RP = CA/PQ

By SSS similarity criterion,

Î”ABC ~ Î”QRP

(iii) Given, in Î”LMP and Î”DEF,

LM = 2.7, MP = 2, LP = 3, EF = 5, DE = 4, DF = 6

MP/DE = 2/4 = 1/2

PL/DF = 3/6 = 1/2

LM/EF = 2.7/5 = 27/50

Here , MP/DE = PL/DF â‰  LM/EF

Therefore, Î”LMP and Î”DEF are not similar.

(iv) In Î”MNL and Î”QPR, it is given,

MN/QP = ML/QR = 1/2

âˆ M = âˆ Q = 70Â°

Therefore, by SAS similarity criterion

âˆ´ Î”MNL ~ Î”QPR

(v) In Î”ABC and Î”DEF, given that,

AB = 2.5, BC = 3, âˆ A = 80Â°, EF = 6, DF = 5, âˆ F = 80Â°

Here , AB/DF = 2.5/5 = 1/2

And, BC/EF = 3/6 = 1/2

â‡’ âˆ B â‰  âˆ F

Hence, Î”ABC and Î”DEF are not similar.

(vi) In Î”DEF, by sum of angles of triangles, we know that,

âˆ D + âˆ E + âˆ F = 180Â°

â‡’ 70Â° + 80Â° + âˆ F = 180Â°

â‡’ âˆ F = 180Â° â€“ 70Â° â€“ 80Â°

â‡’ âˆ F = 30Â°

Similarly, In Î”PQR,

âˆ P + âˆ Q + âˆ R = 180 (Sum of angles of Î”)

â‡’ âˆ P + 80Â° + 30Â° = 180Â°

â‡’ âˆ P = 180Â° â€“ 80Â° -30Â°

â‡’ âˆ P = 70Â°

Now, comparing both the triangles, Î”DEF and Î”PQR, we have

âˆ D = âˆ P = 70Â°

âˆ F = âˆ Q = 80Â°

âˆ F = âˆ R = 30Â°

Therefore, by AAA similarity criterion,

Hence, Î”DEF ~ Î”PQR

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