State which pairs of triangles 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) 
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Solution and Explanation
(i) \(\angle\)A = \(\angle\)P = 60°
\(\angle\)B = \(\angle\)Q = 80°
\(\angle\)C = \(\angle\)R = 40°
Therefore, ∆ABC ∼ ∆PQR [By AAA similarity criterion]
\(\frac{AB}{QR}=\frac{BC}{RP}=\frac{CA}{PQ}\)
(ii) ΔABC∼ΔQRP [By SSS similarity criterion]
(iii) The given triangles are not similar as the corresponding sides are not proportional.
(iv) The given triangles are not similar as the corresponding sides are not proportional.
(v) The given triangles are not similar as the corresponding sides are not proportional.
(vi) In ∆DEF,
\(\angle\)D +\(\angle\)E +\(\angle\)F = 180º (Sum of the measures of the angles of a triangle is 180º.)
70º + 80º +\(\angle\)F = 180º \(\angle\)F = 30º Similarly, in ∆PQR, \(\angle\)P +\(\angle\)Q +\(\angle\)R = 180º (Sum of the measures of the angles of a triangle is 180º.)
\(\angle\)P + 80º +30º = 180º
\(\angle\)P = 70º
In ∆DEF and ∆PQR,
\(\angle\)D = \(\angle\)P (Each 70°)
\(\angle\)E = \(\angle\)Q (Each 80°)
\(\angle\)F = \(\angle\)R (Each 30°)
∴ ∆DEF ∼ ∆PQR [By AAA similarity criterion]
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- \(140\)
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Top CBSE X Triangles Questions
Fill in the blanks using the correct word given in the brackets :
(i) All circles are __________. (congruent, similar)
(ii) All squares are __________. (similar, congruent)
(iii) All __________ triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are __________ and (b) their corresponding sides are __________. (equal, proportional)- Give two different examples of a pair of
(i) Similar figures
(ii)Non-similar figures - State whether the following quadrilaterals are similar or not:
- In figure below (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).
(i)
(ii)
- E and F are points on the sides of PQ and PR respectively of a ∆PQR. For each of the following cases, state whether EF || QR.
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
(iii)PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm
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