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State which pairs of triangles in the given figures 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 :
Asked by Srinu Last Modified
Answer 
Tasneem
(i) ∠A = ∠P = 60°
∠B = ∠Q = 80°
∠C = ∠R = 40°
Therefore, ΔABC ∼ ΔPQR [By AAA similarity criterion]
(iii)The given triangles are not similar as the corresponding sides are not proportional.
(iv) In ? MNL and ? QPR,
v)The given triangles are not similar as the corresponding sides are not proportional.
(vi) In ΔDEF,
∠D +∠E +∠F = 180º
(Sum of the measures of the angles of a triangle is 180º.)
70º + 80º +∠F = 180º
∠F = 30º
Similarly, in ΔPQR,
∠P +∠Q +∠R = 180º
(Sum of the measures of the angles of a triangle is 180º.)
∠P + 80º +30º = 180º
∠P = 70º
In ΔDEF and ΔPQR,
∠D = ∠P (Each 70°)
∠E = ∠Q (Each 80°)
∠F = ∠R (Each 30°)
∴ ΔDEF ∼ ΔPQR [By AAA similarity criterion]
∠M = ∠Q = 70°
∴?MNL ~ ?QPR [By SAS similarity criterion]
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