### MCQ Questions for Class 10 Maths with Answers Chapter 6 Triangles

Class 10 Maths MCQs for Chapter 6 (Triangles) are available online here with answers. All these objective questions are prepared as per the latest CBSE syllabus and NCERT guidelines. MCQs for Class 10 Maths Chapter 6 are prepared according to the new exam pattern. Solving these multiple-choice questions will help students to score good marks in the board exams

1. Two isosceles triangles have equal angles and their areas are in the ratio 16: 25. The ratio of corresponding heights is:

(A) 4:5

(B) 5:4

(C) 3:2

(D) 5:7

2. In the figure, PB and QA are perpendicular to segment AB. If OA = 5 cm, PO = 7cm and area (ΔQOA) = 150 cm², find the area of ΔPOB.

(A) 233 cm²

(B) 294 cm²

(C) 300 cm²

(D) 420 cm²

3. In a right △ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does not give the ratio of the areas of △ABD and △ACB?

(A) (AB/AC)²

(B) (AD/AB)²

(C) (AB/AD)²

(D) (BD/CB)²

4. If △ ABC ~ △ DEF such that AB = 12 cm and DE = 14 cm. Find the ratio of areas of △ ABC and △ DEF.

(A) 49/9

(B) 36/49

(C) 49/16

(D) 25/49

5. In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —

(A) 9: 16

(B) 4:3

(C) 3:4

(D) 16:9

6. ABCD is a parallelogram with diagonal AC If a line XY is drawn such that XY ∥ AB. BX/XC=?

(A) (AY/AC)

(B) DZ/AZ

(C) AZ/ZD

(D) AC/AY

7. D and E are points on the sides AB and AC respectively of a △ABC such that DE || BC. Which of the following statement is true?

(i) △ ADE ~ △ ABC

(ii) (area of △ ADE/ area of △ ABC) = (AD²/AB²)

(iii) (area of △ ADE/ area of △ ABC)= (AB²/ AD²)

(A) only (iii)

(B) only (i)

(C) only (i) and (ii)

(D) all (i) , (ii) and (iii)

8. In ABC, Given that DE//BC, D is the midpoint of AB and E is a midpoint of AC. The ratio AE: EC is __.

(A) 1: 3

(B) 1:1

(C) 2:1

(D) 1:2

9. In ΔABC, AC = 15 cm and DE || BC. If AB/AD=3, Find EC.

(A) 5cm

(B) 10 cm

(C) 2.5cm

(D) 9cm

10. △ ABC is an acute angled triangle. DE is drawn parallel to BC as shown. Which of the following are always true?

i) △ ABC ∼ △ ADE

ii) AD/BD= AE/EC

iii) DE= BC/2

(A) Only (i)

(B) (i) and (ii) only

(C) (i), (ii) and (iii)

(D) (ii) and (iii) only

11. In △ ABC and △ DEF, ∠A = ∠E = 40∘ and AB/ED=AC/EF. Find ∠B if ∠F is 65°

(A) 85°

(B) 75°

(C) 35°

(D) 65°

12. The triangles ABC and ADE are similar, Which of the following is true?

(A) EC/AC=AD/DE

(B) BC/BD=CE/DE

(C) AB/AD=BC/DE

(D) All of the Above

13. The ratio of the corresponding sides of two similar triangles is 1: 3. The ratio of their corresponding heights is

(A) 1:3

(B) 3:1

(C) 1:9

(D) 9:1

14. If in △ CAB and △ FED, AB/ EF=BC/FD=AC/ED, then:

(A) △ ABC∼△ DEF

(B) △ CAB∼△ DEF

(C) △ ABC∼△ EFD

(D) △ CAB∼△ EFD

15. A tower of height 24m casts a shadow 50m and at the same time, a girl of height 1.8m casts a shadow. Find the length of the shadow of girl.

(A) 3.75m

(B) 3.5m

(C) 3.25m

(D) 3m

16. In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB = 120°, then the correct relation is-

(A) a² = b² + c² – bc

(B) a² = b² + c² + bc

(C) a² = b² + c² – 2bc

(D) a² = b² + c² + 2bc

17. If the distance between the top of two trees 20 m and 28 m tall is 17 m, then the horizontal distance between the trees is :

(A) 11m

(B) 31m

(C) 15m

(D) 9m

18. In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

(A) AD²=DC×AC

(B) AB²=AD×AC

(C) AB²=AD×DC

(D) AB²=DC²+AD²

19. If Δ ABC and Δ DEF are similar such that 2AB = DE and BC = 8 cm, then Find EF.

(A) 16 cm

(B) 12 cm

(C) 8 cm

(D) 4 cm

20. △ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm.△ DEF is similar to △ABC. If EF = 4 cm, then the perimeter of △DEF is –

(A) 7.5 cm

(B) 15cm

(C) 30cm

(D) 22.5cm

21. O is a point on side PQ of a APQR such that PO = QO = RO, then

(a) RS² = PR × QR

(b) PR² + QR² = PQ²

(c) QR² = QO² + RO²

(d) PO² + RO² = PR²

22. In ABC, DE || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to

(a) 7.5 cm

(b) 3 cm

(c) 4.5 cm

(d) 6 cm

### MCQ Questions for Class 10 Maths with Answers Chapter 6 Triangles

23. Triangle ABC is an equilateral triangle of side a. Its area will be…

24. In a square of side 10 cm, its diagonal = …

(a) 15 cm

(b) 10√2 cm

(c) 20 cm

(d) 12 cm

25. In a rectangle Length = 8 cm, Breadth = 6 cm. Then its diagonal = …

(a) 9 cm

(b) 14 cm

(c) 10 cm

(d) 12 cm

26. In a rhombus if d1 = 16 cm, d2 = 12 cm, its area will be…

(a) 16 × 12 cm²

(b) 96 cm²

(c) 8 × 6 cm²

(d) 144 cm²

27. In a rhombus if d1 = 16 cm, d2 = 12 cm, then the length of the side of the rhombus is

(a) 8 cm

(b) 9 cm

(c) 10 cm

(d) 12 cm

28. If in two triangles ABC and DEF, AB/DF=BC/FE=CA/ED, then

(a) ∆ABC ~ ∆DEF

(b) ∆ABC ~ ∆EDF

(c) ∆ABC ~ ∆EFD

(d) ∆ABC ~ ∆DFE

29. In ∠BAC = 90° and AD ⊥ BC. A Then

(а) BD.CD = BC²

(б) AB.AC = BC²

(c) BD.CD = AD²

(d) AB.AC = AD²

30. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is

(a) 2.5

(b) 3

(c) 5

(d) 6

31. If ΔABC ~ ΔDEF and ΔABC is not similar to ΔDEF then which of the following is not true?

(a) BC.EF = AC.FD

(b) AB.ED = AC.DE

(c) BC.DE = AB.EE

(d) BC.DE = AB.FD

32. If in two triangles DEF and PQR, ZD = ZQ and ZR = ZE, then which of the following is not true?

33. If in triangles ABC and DEF,AB/DE=BC/FD , then they will be similar, if

(a) ∠B = ∠E

(b) ∠A = ∠D

(c) ∠B = ∠D

(d) ∠A = ∠F

34. In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is:

(a) 18

(b) 16

(c) 19

(d) 12

35. In the given figure, value of x(in cm) is

(a) 4

(b) 5

(c) 6

(d) 8

36. In the given figure ΔABC ~ ΔPQR. The value of x is

(a) 2.5 cm

(b) 3.5 cm

(c) 2.75 cm

(d) 3 cm

37. In ΔABC, if DE || BC, AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then value of x is

(a) 3

(b) 4

(c) 5

(d) 3.

38. The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then AB equals

(a) 6 cm

(b) 10 cm

(c) 15 cm

(d) 24 cm

39. If ΔABC is similar to ΔDEF such that 2 AB = DE and BC = 8 cm then EF is equal to.

(a) 12 cm

(b) 4 cm

(c) 16 cm

(d) 8 c

40. In ΔABC, AB = 6 cm and DE || BC such that AE = 14 AC then the length of AD is

(a) 2 cm

(b) 1.2 cm

(c) 1.5 cm

(d) 4 cm

41. In the given figure DE || AC which of the following is true?

(a) x = (a+b)/ay

(b) y = ax/(a+b)

(c) x = ay/(a+b)

(d) xy = ab

42. ΔABC ~ ΔDEF. If AB = 4 cm, BC = 3.5 cm, CA = 2.5 cm and DF = 7.5 cm, then the perimeter of ΔDEF is

(a) 10 cm

(b) 14 cm

(c) 30 cm

(d) 25 cm

43. In the figure PQ || BC. If PQ/BC = 25 then AP/PB is

(a) 2/5

(b) 2/3

(c) 3/2

(c) 3/5

44. In the given figure, ΔACB ~ ΔAPQ. If AB = 6 cm, BC = 8 cm, and PQ = 4 cm then AQ is equal to

(a) 2 cm

(b) 2.5 cm

(c) 3 cm

(d) 3.5 cm

45. ΔDEF ~ ΔABC. If DE : AB = 2 : 3 and ar ΔDEF is equal to 44 square units then ar (ΔABC) (square unit) is

(a) 99

(b) 120

(c) 1769

(d) 66

46. ΔABC and ΔBDE are two equilateral triangles such that D is the mid point of BC. Ratio of the areas of triangle ΔABC and ΔBDE is.

(a) 2 : 1

(b) 1 : 2

(c) 4 : 1

(d) 1 : 4

47. If ΔABC ~ ΔPQR, arΔABC/arΔPQR = 94 and AB = 18 cm, then the length of PQ is

(a) 14 cm

(b) 8 cm

(c) 10 cm

(d) 12 cm

48. In the given figure ΔABC ~ ΔPQR, PM is median of ΔPQR. If ar ΔABC = 289 cm², BC = 17 cm, MR = 6.5 cm then the area of ΔPQM is

(a) 169 cm²

(b) 13 cm²

(c) 84.5 cm²

(d) 144.5 cm²

49. If the ratio of the perimeters of two similar triangles is 4 : 25, then the ratio of the areas of the similar triangles is

(a) 16 : 625

(b) 2 : 5

(c) 5 : 2

(d) 625 : 16

50. In the given figure, PQ = 24 cm, QR = 26 cm ∠PAR = 90°, PA = 6 cm, and AR = 8 cm, the degree measure of ∠QPR is

(a) 90°

(b) 100°

(c) 50°

(d) 45°

51. In the given figure the value of x is

(a) 4 cm

(b) 5 cm

(c) 8 cm

(d) 3 cm

52. ΔPQR is an equilateral triangle with each side of length 2p. If PS ⊥ QR, then PS is equal to

(a) (√3/2)p

(b) 2p

(c) √3p

(d) p

53. In ΔLMN, ∠L = 50° and ∠N = 60°, If ΔLMN ~ ΔPQR, then find ∠Q

(a) 50°

(b) 70°

(c) 60°

(d) 40⁰

MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8