Respuesta :
Similarity Criteria: Two Triangles are similar, if any one of the similarity criteria (AAA), (SSS), (SAS) is satisfied.
Two triangles are similar, if:
Their corresponding angles are equal. Their corresponding sides are in the same ratio.
(i)
Yes, the pair of triangles are similar.
In ΔABC and ΔPQR,
∠A = ∠P = 60° (Given)
∠B = ∠Q = 80° (Given)
∠C = ∠R = 40° (Given)
∴ ΔABC ~ ΔPQR (AAA similarity criterion)
(ii)
Yes, the pair of triangles are similar.
In ΔABC and ΔPQR,
AB/QR = 2/4= 1/2 = BC/RP = 2.5 / 5=1/2 =CA/PQ =3/6=1/2
∴ ΔABC ~ ΔQRP (SSS similarity criterion)
(iii)
No, the pair of triangles are not similar.
In ΔLMP and ΔDEF,
LM = 2.7, MP = 2, LP = 3, EF = 5, DE = 4, DF = 6
MP/EF = 2/5
LP/DF = 3/6 = 1/2
LM/DE= 2.7/4 =
Here, MP/EF≠ LP/DF ≠ LM/DE
Hence, ΔLMP and ΔDEF are not similar.
(iv)
Yes, the pair of triangles are similar.
In ΔMNL and ΔQPR, we have
MN/QP = ML/QR = 1/2
∠M = ∠Q = 70°
∴ ΔMNL ~ ΔQPR (SAS similarity criterion)
(v)
No, the pair of triangles are not similar.
In ΔABC , ∠A is given but the included side AC is not given.
Hence, ΔABC and ΔDEF are not similar.
(vi)
Yes, the pair of triangles are similar.
In ΔDEF,we have
∠D + ∠E + ∠F = 180° (sum of angles of a triangle)
⇒ 70° + 80° + ∠F = 180°
⇒ ∠F = 180° – 70° – 80°
⇒ ∠F = 30°
In PQR, we have
∠P + ∠Q + ∠R = 180 (Sum of angles of Δ)
⇒ ∠P + 80° + 30° = 180°
⇒ ∠P = 180° – 80° -30°
⇒ ∠P = 70°
In ΔDEF and ΔPQR, we have
∠D = ∠P = 70°
∠F = ∠Q = 80°
∠F = ∠R = 30°
Hence, ΔDEF ~ ΔPQR (AAA similarity criterion)
To know more about triangles visit: brainly.com/question/2773823
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