Class 10 Maths – Chapter 6: Triangles (60 MCQs)

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Triangles (Similarity) — 60 MCQs (Interactive)

Triangles (Similarity) — 60 MCQs

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  1. 1
    Two figures having the same shape but not necessarily the same size are called:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Similar figures — Two figures have same shape (not necessarily size).
  2. 2
    All congruent figures are:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Similar — congruence implies similarity.
  3. 3
    All circles are:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Similar — all circles have same shape.
  4. 4
    All squares are:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Similar only — squares of different sizes are similar; congruent only if side lengths equal.
  5. 5
    All equilateral triangles are:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Similar — equilateral triangles have same angles.
  6. 6
    A square and a rhombus are not similar because:
    Correct ✅
    Incorrect ✖
    Answer
    (c) Both — shape differs unless it's a square (special rhombus).
  7. 7
    Two polygons of the same number of sides are similar if:
    Correct ✅
    Incorrect ✖
    Answer
    (c) Both — both conditions required for polygon similarity.
  8. 8
    The constant ratio of corresponding sides of similar figures is called:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Scale factor — also called representative fraction.
  9. 9
    World maps are drawn using:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Similarity — maps use scales (similarity ratios).
  10. 10
    The shadow of an object forms:
    Correct ✅
    Incorrect ✖
    Answer
    (b) A similar figure — shadow keeps shape, scales size.
  11. 11
    If one polygon is similar to a second and the second is similar to a third, then:
    Correct ✅
    Incorrect ✖
    Answer
    (b) First and third are similar — similarity is transitive.
  12. 12
    In quadrilaterals, equality of corresponding angles alone is:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Not sufficient — sides must also be proportional.
  13. 13
    In quadrilaterals, proportionality of corresponding sides alone is:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Not sufficient — angles must match too for polygon similarity.
  14. 14
    A photograph of the same object printed in different sizes shows:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Similarity — shape preserved, size changed by scale factor.
  15. 15
    Scale factor of a figure enlarged from 35 mm to 45 mm is:
    Correct ✅
    Incorrect ✖
    Answer
    (a) 45/35 — new length divided by original length.
  16. 16
    Two triangles are similar if:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Both conditions — equal angles and proportional sides.
  17. 17
    Equiangular triangles are always:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Similar — same angles imply proportional sides (Thales/BPT idea).
  18. 18
    Thales’ theorem is also called:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Basic Proportionality Theorem — line parallel to one side divides other sides proportionally.
  19. 19
    In ΔABC, DE ∥ BC ⇒ AD/DB =:
    Correct ✅
    Incorrect ✖
    Answer
    (a) AE/EC — Basic Proportionality Theorem result.
  20. 20
    Theorem 6.1 states:
    Correct ✅
    Incorrect ✖
    Answer
    (a) That is exactly Theorem 6.1 (Basic Proportionality Theorem).
  21. 21
    Converse of Theorem 6.1 (Theorem 6.2):
    Correct ✅
    Incorrect ✖
    Answer
    (a) Theorem 6.2 is the converse: equal ratios imply parallel.
  22. 22
    A trapezium ABCD with AB ∥ DC and EF ∥ AB, then:
    Correct ✅
    Incorrect ✖
    Answer
    (a) AE/ED = BF/FC — from similar triangles in trapezium construction.
  23. 23
    If PS/SQ = PT/TR and ∠PST = ∠PRQ, then ΔPQR is:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Isosceles — leads to equal base angles so two sides equal.
  24. 24
    Using Theorem 6.1, a line through midpoint of one side ∥ another side will:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Bisect third side — median parallel to side bisects the third side.
  25. 25
    If diagonals intersect with AO/BO = CO/DO, the quadrilateral is:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Trapezium — that ratio condition implies one pair of opposite sides parallel.
  26. 26
    If DE ∥ BC in ΔABC ⇒ AD/AB =:
    Correct ✅
    Incorrect ✖
    Answer
    (a) AE/AC — rearranged from theorem result AD/AB = AE/AC.
  27. 27
    If a line divides two sides in equal ratio, it must be:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Parallel to third side — converse of BPT.
  28. 28
    The symbol used for similarity of triangles:
    Correct ✅
    Incorrect ✖
    Answer
    (c) ~ — e.g., ΔABC ~ ΔDEF.
  29. 29
    ΔABC ~ ΔDEF implies:
    Correct ✅
    Incorrect ✖
    Answer
    (c) Both — corresponding angles equal and sides proportional.
  30. 30
    Similarity relation must always be written with:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Correct correspondence — order matters to show which vertex corresponds to which.
  31. 31
    AAA criterion means:
    Correct ✅
    Incorrect ✖
    Answer
    (b) AAA — equal angles imply similarity.
  32. 32
    AA criterion states:
    Correct ✅
    Incorrect ✖
    Answer
    (a) AA — two angles equal implies third equal by angle sum; triangles similar.
  33. 33
    SSS similarity criterion means:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Sides proportional ⇒ angles equal ⇒ similarity.
  34. 34
    SAS similarity criterion states:
    Correct ✅
    Incorrect ✖
    Answer
    (a) SAS — equal included angle + proportional adjacent sides.
  35. 35
    RHS similarity criterion applies to:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Right triangles only — hypotenuse and one side proportional gives similarity.
  36. 36
    If AB/DE = AC/DF and ∠A = ∠D ⇒ ΔABC ~ ΔDEF by:
    Correct ✅
    Incorrect ✖
    Answer
    (a) SAS similarity.
  37. 37
    If ΔABC ~ ΔPQR ⇒ then CM/RN =:
    Correct ✅
    Incorrect ✖
    Answer
    (c) Both — medians scale same as corresponding sides in similar triangles.
  38. 38
    In ΔABC and ΔDEF, if ∠A = ∠D, ∠B = ∠E, ∠C = ∠F ⇒ triangles similar by:
    Correct ✅
    Incorrect ✖
    Answer
    (b) AAA — equal corresponding angles imply similarity.
  39. 39
    If AB/DE = BC/EF = AC/DF ⇒ triangles are similar by:
    Correct ✅
    Incorrect ✖
    Answer
    (a) SSS similarity criterion.
  40. 40
    In ΔABC and ΔPQR, if ∠A = ∠P and AB/PQ = AC/PR ⇒ similarity criterion is:
    Correct ✅
    Incorrect ✖
    Answer
    (a) SAS — included angle and adjacent sides proportional.
  41. 41
    In two right triangles, if hypotenuse and one side proportional ⇒ triangles similar by:
    Correct ✅
    Incorrect ✖
    Answer
    (b) RHS — right triangle similarity criterion.
  42. 42
    ΔPOQ ~ ΔSOR if PQ ∥ RS because:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Because PQ ∥ RS gives corresponding equal angles (alternate & vertical).
  43. 43
    If ΔABC ~ ΔRQP ⇒ ∠C = ∠P due to:
    Correct ✅
    Incorrect ✖
    Answer
    (a) AAA — corresponding angles equal in similar triangles.
  44. 44
    A 6 m pole casts 4 m shadow; tower casts 28 m shadow ⇒ height of tower is:
    Correct ✅
    Incorrect ✖
    Answer
    Scale factor = 28/4 = 7; tower height = 6 * 7 = 42 m ⇒ (b).
  45. 45
    A girl of height 90 cm, lamp-post of 3.6 m ⇒ after 4 s walking (4.8 m away), shadow length =:
    Correct ✅
    Incorrect ✖
    Answer
    Using similar triangles: (4.8+x)/x = 3.6/0.9 = 4 ⇒ x = 1.6 m ⇒ (b).
  46. 46
    Similarity is based on:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Shape — similar figures have same shape (sizes may differ).
  47. 47
    Congruence implies:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Similarity always — congruent figures are same shape and size, hence similar.
  48. 48
    Two photos of same person (age 10 and 40) are:
    Correct ✅
    Incorrect ✖
    Answer
    (b) Not similar — shape changes with age even if sizes are same.
  49. 49
    A square and rectangle are not similar because:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Sides not proportional — rectangle sides ratio differs from 1:1 of square.
  50. 50
    A line parallel to one side of triangle divides:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Other two sides proportionally — Basic Proportionality Theorem.
  51. 51
    In ΔABC, DE ∥ BC ⇒ AD/DB = AE/EC shows:
    Correct ✅
    Incorrect ✖
    Answer
    (a) BPT — Basic Proportionality Theorem.
  52. 52
    The converse of Basic Proportionality Theorem is:
    Correct ✅
    Incorrect ✖
    Answer
    (a) That is Theorem 6.2, the converse.
  53. 53
    Triangles are denoted similar using symbol:
    Correct ✅
    Incorrect ✖
    Answer
    (a) ~ — e.g., ΔABC ~ ΔDEF.
  54. 54
    In similar triangles, ratio of altitudes is equal to:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Ratio of sides — all linear measures scale by same factor.
  55. 55
    If ΔABC ~ ΔPQR ⇒ then ratio of medians =:
    Correct ✅
    Incorrect ✖
    Answer
    (c) Both — medians scale in same ratio as corresponding sides.
  56. 56
    If ΔABC ~ ΔPQR ⇒ then ratio of perimeters =:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Ratio of sides — perimeter scales by the same linear ratio.
  57. 57
    If ΔABC ~ ΔPQR ⇒ then ratio of areas =:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Square of side ratio — area scales with square of linear scale factor.
  58. 58
    The scale factor is also called:
    Correct ✅
    Incorrect ✖
    Answer
    (a) Representative Fraction — often used in maps/blueprints.
  59. 59
    Example of indirect measurement using similarity:
    Correct ✅
    Incorrect ✖
    Answer
    (c) Both — indirect measurements often use similar triangles/ratio methods.
  60. 60
    Which theorem is applied in proving Pythagoras theorem using similarity?
    Correct ✅
    Incorrect ✖
    Answer
    (c) AAA/Similarity arguments — similarity of triangles is used in many proofs of Pythagoras.
Prepared from NCERT Class 10 — Chapter: Triangles (Similarity). Use the Reset All button to clear all answers.

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