Question 1 State which pairs of triangles in the following 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: (i) (ii) (iii) (iv) (v) (vi)
Class 10 - Math - Triangles Page 138
Answers
Similarity Criteria:
Two Triangles are similar ,if any one of the similarity criterion (AAA), (SSS), (SAS) is satisfied.
All congruent figures are similar, but it does not mean that all similar figures are congruent.
Two polygons of the same number of sides are similar, if:
Their corresponding angles are equal.Their corresponding sides are in the same ratio.
Two triangles are similar, if:
Their corresponding angles are equal.Their corresponding sides are in the same ratio.
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Solution:
(i)
Yes, the pair of triangles is 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 is 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 is 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 is 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°
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Figure is in the attachment....
Hope this will help you.......
Answer:
Step-by-step explanation:
There are three criterion’s aaa sss sas u can use by using the basic proportionality theorem and converse of it and then sss and aa theorem to prove any problems u need to have knowledge
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