MATHEMATICS CLASS- 10

MCQ- CH-6(Triangles)

CBSEChapter 6MCQ's

Class 10 Mathematics

Chapter 6: Triangles

50 Board-Level MCQs with Answers and Solutions

Q1. If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in

(a) Equal lengths
(b) Same ratio
(c) Different ratio
(d) No fixed ratio

Answer: (b) Same ratio

Solution: This is the Basic Proportionality Theorem (BPT).

Q2. In ΔABC, if DE || BC, then

(a) AD/DB = AE/EC
(b) AD = DB
(c) AE = EC
(d) AB = AC

Answer: (a)

Q3. Two triangles are similar if their corresponding

(a) Sides are equal
(b) Angles are equal and sides proportional
(c) Areas are equal
(d) Perimeters are equal

Answer: (b)

Q4. Which criterion is used for similarity of triangles?

(a) SSS
(b) SAS
(c) AA
(d) All of these

Answer: (d)

Q5. If two angles of one triangle are equal to two angles of another triangle, then the triangles are

(a) Congruent
(b) Similar
(c) Isosceles
(d) Right-angled

Answer: (b)

Q6. If ΔABC ~ ΔDEF, then

(a) AB/DE = BC/EF = AC/DF
(b) AB = DE
(c) BC = EF
(d) AC = DF

Answer: (a)

Q7. If the corresponding sides of two triangles are proportional, then the triangles are similar by

(a) AA
(b) SAS
(c) SSS
(d) RHS

Answer: (c)

Q8. The ratio of areas of two similar triangles is equal to

(a) Ratio of corresponding sides
(b) Square of ratio of corresponding sides
(c) Cube of ratio of corresponding sides
(d) Product of corresponding sides

Answer: (b)

Q9. If two similar triangles have side ratio 2 : 3, then their area ratio is

(a) 2 : 3
(b) 4 : 9
(c) 8 : 27
(d) 3 : 2

Answer: (b)

Q10. In a right triangle, the square of the hypotenuse is equal to

(a) Sum of squares of other two sides
(b) Difference of squares of sides
(c) Product of sides
(d) Twice the area

Answer: (a)

Solution: Pythagoras Theorem.

Q11. The hypotenuse of a right triangle with sides 6 cm and 8 cm is

(a) 9 cm
(b) 10 cm
(c) 12 cm
(d) 14 cm

Answer: (b)

Solution: √(6² + 8²) = √100 = 10 cm.

Q12. Which of the following is a Pythagorean triplet?

(a) 3, 4, 5
(b) 5, 6, 7
(c) 2, 3, 4
(d) 4, 5, 6

Answer: (a)

Q13. If ΔABC ~ ΔDEF and AB = 8 cm, DE = 12 cm, then the scale factor is

(a) 2/3
(b) 3/2
(c) 4/3
(d) 5/3

Answer: (a)

Q14. If two triangles are similar, then their corresponding angles are

(a) Supplementary
(b) Complementary
(c) Equal
(d) Unequal

Answer: (c)

Q15. If ΔABC ~ ΔPQR, then ∠B =

(a) ∠P
(b) ∠Q
(c) ∠R
(d) Cannot be determined

Answer: (b)

Q16. In ΔABC, if DE || BC and AD = 4 cm, DB = 6 cm, then AD/AB equals

(a) 2/5
(b) 3/5
(c) 4/5
(d) 5/6

Answer: (a)

Solution: AB = 4 + 6 = 10, so AD/AB = 4/10 = 2/5.

Q17. If two triangles are similar, their perimeters are in the ratio

(a) Square of sides ratio
(b) Same as sides ratio
(c) Cube of sides ratio
(d) Inverse ratio

Answer: (b)

Q18. Which criterion is not used for similarity?

(a) AA
(b) SAS
(c) SSS
(d) RHS

Answer: (d)

Q19. If one angle of a triangle is 90°, then the triangle is

(a) Acute triangle
(b) Obtuse triangle
(c) Right triangle
(d) Equilateral triangle

Answer: (c)

Q20. The converse of Pythagoras theorem helps to determine whether a triangle is

(a) Similar
(b) Isosceles
(c) Right-angled
(d) Equilateral

Answer: (c)

Q21. If 5² + 12² = 13², then the triangle is

(a) Acute-angled
(b) Obtuse-angled
(c) Right-angled
(d) Equilateral

Answer: (c)

Q22. If the corresponding sides of two similar triangles are in the ratio 3 : 5, then their perimeter ratio is

(a) 9 : 25
(b) 3 : 5
(c) 27 : 125
(d) 5 : 3

Answer: (b)

Q23. If ΔABC ~ ΔDEF and BC = 12 cm, EF = 18 cm, then BC/EF equals

(a) 2/3
(b) 3/2
(c) 4/3
(d) 1/2

Answer: (a)

Q24. A line parallel to one side of a triangle forms

(a) Congruent triangles
(b) Similar triangles
(c) Equal triangles
(d) Right triangles

Answer: (b)

Q25. The area ratio of similar triangles with side ratio 4 : 7 is

(a) 4 : 7
(b) 8 : 14
(c) 16 : 49
(d) 64 : 343

Answer: (c)

Q26. (CBSE PYQ) If ΔABC ~ ΔDEF and AB = 6 cm, DE = 9 cm, AC = 8 cm, then DF is

(a) 10 cm
(b) 12 cm
(c) 14 cm
(d) 16 cm

Answer: (b)

Solution: 6/9 = 8/DF ⇒ DF = 12 cm.

Q27. If a line divides two sides of a triangle in the same ratio, then the line is

(a) Perpendicular
(b) Parallel to third side
(c) Median
(d) Angle bisector

Answer: (b)

Q28. The longest side of a right triangle is called

(a) Base
(b) Altitude
(c) Hypotenuse
(d) Median

Answer: (c)

Q29. If the sides of a triangle are 8 cm, 15 cm and 17 cm, then it is

(a) Acute triangle
(b) Obtuse triangle
(c) Right triangle
(d) Equilateral triangle

Answer: (c)

Q30. Which theorem relates the sides of a right triangle?

(a) BPT
(b) Pythagoras Theorem
(c) Midpoint Theorem
(d) Thales Theorem

Answer: (b)

Q31. If side ratio of two similar triangles is 5 : 6, then area ratio is

(a) 5 : 6
(b) 25 : 36
(c) 125 : 216
(d) 36 : 25

Answer: (b)

Q32. The converse of BPT is used to prove that a line is

(a) Perpendicular
(b) Parallel
(c) Equal
(d) Bisector

Answer: (b)

Q33. Which of the following triangles are always similar?

(a) Two equilateral triangles
(b) Two isosceles triangles
(c) Two scalene triangles
(d) Two right triangles

Answer: (a)

Q34. If ΔABC ~ ΔDEF and their area ratio is 25 : 36, then side ratio is

(a) 25 : 36
(b) 5 : 6
(c) 10 : 12
(d) 36 : 25

Answer: (b)

Q35. If the sides of a triangle are 7 cm, 24 cm and 25 cm, then it is

(a) Acute triangle
(b) Obtuse triangle
(c) Right triangle
(d) Isosceles triangle

Answer: (c)

Q36. (CBSE PYQ) In similar triangles, the ratio of corresponding medians is equal to

(a) Area ratio
(b) Side ratio
(c) Square of side ratio
(d) Cube of side ratio

Answer: (b)

Q37. If one angle of a triangle is 60° and all sides are equal, the triangle is

(a) Scalene
(b) Isosceles
(c) Equilateral
(d) Right triangle

Answer: (c)

Q38. If two triangles have one equal angle and including sides proportional, then they are similar by

(a) AA
(b) SAS
(c) SSS
(d) RHS

Answer: (b)

Q39. The side opposite the right angle is

(a) Base
(b) Altitude
(c) Hypotenuse
(d) Median

Answer: (c)

Q40. If the side ratio of similar triangles is 1 : 4, then area ratio is

(a) 1 : 4
(b) 1 : 8
(c) 1 : 16
(d) 1 : 64

Answer: (c)

Q41. Which of the following is not a Pythagorean triplet?

(a) 3, 4, 5
(b) 5, 12, 13
(c) 8, 15, 17
(d) 6, 8, 11

Answer: (d)

Q42. If ΔABC ~ ΔPQR and AB = 10 cm, PQ = 15 cm, then scale factor is

(a) 2/3
(b) 3/2
(c) 5/2
(d) 4/3

Answer: (a)

Q43. A right triangle has sides 9 cm and 12 cm. Its hypotenuse is

(a) 13 cm
(b) 14 cm
(c) 15 cm
(d) 16 cm

Answer: (c)

Q44. The ratio of corresponding altitudes of similar triangles equals

(a) Side ratio
(b) Area ratio
(c) Square of side ratio
(d) Cube of side ratio

Answer: (a)

Q45. If two triangles are similar, their corresponding sides are

(a) Equal
(b) Proportional
(c) Perpendicular
(d) Parallel

Answer: (b)

Q46. (CBSE PYQ) The area ratio of two similar triangles is 49 : 64. The ratio of corresponding sides is

(a) 49 : 64
(b) 7 : 8
(c) 14 : 16
(d) 21 : 24

Answer: (b)

Q47. If DE || BC in ΔABC, then triangles ADE and ABC are

(a) Congruent
(b) Similar
(c) Equal in area
(d) Right triangles

Answer: (b)

Q48. A triangle with sides 9 cm, 40 cm and 41 cm is

(a) Acute triangle
(b) Obtuse triangle
(c) Right triangle
(d) Equilateral triangle

Answer: (c)

Q49. If the ratio of areas of two similar triangles is 81 : 121, then the ratio of corresponding sides is

(a) 9 : 11
(b) 81 : 121
(c) 18 : 22
(d) 27 : 33

Answer: (a)

Q50. Which statement is true?

(a) Similar triangles are always congruent.
(b) Congruent triangles are always similar.
(c) Similar triangles have equal areas.
(d) Similar triangles have equal corresponding sides.

Answer: (b) Congruent triangles are always similar.

Solution: Congruent triangles have equal corresponding sides and angles, so they satisfy the conditions for similarity.