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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 ΔABC and ΔPQR,

    ∠A = ∠P = 60°

    ∠B = ∠Q = 80°

    ∠C = ∠R = 40°

    Therefore by AAA similarity criterion,

    ∴ ΔABC ~ ΔPQR

    (ii) Given, in ΔABC and ΔPQR,

    AB/QR = BC/RP = CA/PQ

    By SSS similarity criterion,

    ΔABC ~ ΔQRP

    (iii) Given, in ΔLMP and ΔDEF,

    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 ≠ LM/EF

    Therefore, ΔLMP and ΔDEF are not similar.

    (iv) In ΔMNL and ΔQPR, it is given,

    MN/QP = ML/QR = 1/2

    ∠M = ∠Q = 70°

    Therefore, by SAS similarity criterion

    ∴ ΔMNL ~ ΔQPR

    (v) In ΔABC and ΔDEF, given that,

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

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

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

    ⇒ ∠B ≠ ∠F

    Hence, ΔABC and ΔDEF are not similar.

    (vi) In ΔDEF, by sum of angles of triangles, we know that,

    ∠D + ∠E + ∠F = 180°

    ⇒ 70° + 80° + ∠F = 180°

    ⇒ ∠F = 180° – 70° – 80°

    ⇒ ∠F = 30°

    Similarly, In ΔPQR,

    ∠P + ∠Q + ∠R = 180 (Sum of angles of Δ)

    ⇒ ∠P + 80° + 30° = 180°

    ⇒ ∠P = 180° – 80° -30°

    ⇒ ∠P = 70°

    Now, comparing both the triangles, ΔDEF and ΔPQR, we have

    ∠D = ∠P = 70°

    ∠F = ∠Q = 80°

    ∠F = ∠R = 30°

    Therefore, by AAA similarity criterion,

    Hence, ΔDEF ~ ΔPQR

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