Class 10 Maths MCQs Chapter 6 Triangles

1. 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

2. 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

3. AABC is an equilateral A of side a. Its area will be…

4. In a square of side 10 cm, its diagonal = …
(a) 15 cm
(b) 10√2 cm
(c) 20 cm
(d) 12 cm

5. In a rectangle Length = 8 cm, Breadth = 6 cm. Then its diagonal = …
(a) 9 cm
(b) 14 cm
(c) 10 cm
(d) 12 cm

6. 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

7. 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

8. If in two As ABC and DEF, \(\frac{\mathrm{AB}}{\mathrm{DF}}=\frac{\mathrm{BC}}{\mathrm{FE}}=\frac{\mathrm{CA}}{\mathrm{ED}}\), then
(a) ∆ABC ~ ∆DEF
(b) ∆ABC ~ ∆EDF
(c) ∆ABC ~ ∆EFD
(d) ∆ABC ~ ∆DFE

9. It is given that ∆ABC ~ ∆DEF and \(\frac{\mathrm{BC}}{\mathrm{EF}}=\frac{1}{5}\). Then \(\frac{\operatorname{ar}(D E F)}{\operatorname{ar}(A B C)}\) is equal to
(а) 5
(b) 25
(c) \(\frac{1}{25}\)
(d) \(\frac{1}{5}\)

10. In ∠BAC = 90° and AD ⊥ BC. A Then

(а) BD.CD = BC²
(б) AB.AC = BC²
(c) BD.CD = AD²
(d) AB.AC = AD²

11. 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

12. 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

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

14. If ΔABC ~ ΔPQR, \(\frac{\mathrm{BC}}{\mathrm{QR}}=\frac{1}{3}\) then \(\frac{\operatorname{ar}(PQR)}{\operatorname{ar}(BCA)}\) is
(a) 9
(b) 3
(c) 1/3
(d) 1/9

15. If ΔABC ~ ΔQRP, \(\frac{\operatorname{ar}(\mathrm{ABC})}{\operatorname{ar}(\mathrm{PQR})}=\frac{9}{4}\), AB = 18 cm and BC = 15 cm, then PR is equal to
(a) 10 cm
(b) 12 cm
(c) \(\frac{20}{3}\)cm
(d) 8 cm

16. If in triangles ABC and DEF,\(\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}}\) , then they will be similar, if
(a) ∠B = ∠E
(b) ∠A = ∠D
(c) ∠B = ∠D
(d) ∠A = ∠F

17. In the given figure, \(\frac{\mathrm{AD}}{\mathrm{BD}}=\frac{\mathrm{AE}}{\mathrm{EC}}\) and ∠ADC = 70° ∠BAC =

(a) 70°
(b) 50°
(c) 80°
(d) 60°

18. In given figure, AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm, BF = 2.5 cm, then

(a) DE || BC
(b) DF || AC
(c) EF || AB
(d) none of these

19. If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true? [NCERT Exemplar Problems] (a) BC . EF = AC . FD
(b) AB . EF = AC . DE
(c) BC . DE = AB . EF
(d) BC . DE = AB . FD

20. If in two triangles ABC and PQR, \(\frac{\mathrm{AB}}{\mathrm{QR}}=\frac{\mathrm{BC}}{\mathrm{PR}}=\frac{\mathrm{CA}}{\mathrm{PQ}}\), then [NCERT Exemplar Problems] (a) ΔPQR ~ ΔCAB
(b) ΔPQR ~ ΔABC
(c) ΔCBA ~ ΔPQR
(d) ΔBCA ~ ΔPQR

21. Match the column:

(a) 1 → A, 2 → B, 3 → C, 4→ D
(b) 1 → D, 2 → A, 3 → C, 4 → B
(c) 1 → B, 2 → A, 3 → C, 4 → D
(d) 1 → C, 2 → B, 3 → D, 4 → A.

22. In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are [NCERT Exemplar Problems] (a) congruent but not similar
(b) similar but not congruent
(c) neither congruent nor similar
(d) congruent as well as similar

23. If in triangles ABC and DEF, \(\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}}\) then they will be similar, when [NCERT Exemplar Problems] (a) ∠B = ∠E
(b) ∠A = ∠D
(c) ∠B = ∠D
(d) ∠A = ∠F

24. ABC and BDE are two equilateral triangles such that D is mid-point of BC. Ratio of the areas of triangles ABC and BDE is
(a) 2 : 1
(b) 1:4
(c) 1:2
(d) 4:1

25. Sides of two similar triangles are in the ratio 3 : 7. Areas of these triangles are in the ratio
(a) 9 : 35
(b) 9 : 49
(c) 49 : 9
(d) 9 : 42

26. Sides of triangles are (i) 3 cm, 4 cm, 6 cm. (ii) 4 cm, 5 cm, 6 cm. (iii) 7 cm, 24 cm, 25 cm (iv) 5 cm, 12 cm, 14 cm. Which of these is right triangle?
(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

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

28. “If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.” This theorem is known as _____ .

29. In ΔABC, D and E are points on sides AB and AC respectively such that DE || BC and AD : DB = 3 : 1. If EA = 6.6 cm then find AC.

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

31. In the given figure, if ΔABC ~ ΔPQR

The value of x is_____ .

32. The perimeter of two similar triangles ABC and LMN are 60 cm and 48 cm respectively. If LM = 8 cm, then what is the length of AB?

33. In fig. ZM = ZN = 46°, express x in terms of a, b and c, where a, b and c are lengths of LM, MN and NK respectively.

34. ΔABC ~ ΔPQR. Area of ΔABC = 81 cm² and area of ΔPQR =121 cm². If altitude AD = 9 cm, then PM = ______ .

35. Given ΔABC ~ ΔPQR, if \(\frac{A B}{P Q}=\frac{1}{3}\), then find \(\frac{\operatorname{ar} \Delta \mathrm{ABC}}{\operatorname{ar} \Delta \mathrm{PQR}}\). [CBSE 2018]

36. In fig., DE || BC, AD = 1 cm and BD = 2 cm. What is the ratio of the ar(ΔABC) to the ar(ΔADE)? [Delhi 2019]

37. In figure, S and T are points on the sides PQ and PR, respectively of APQR, such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the ratio of the areas of ΔPST and ΔPQR.

38. In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. The angle B is _____ .

39. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is
(a) 9 cm
(b) 10 cm
(c) 8 cm
(d) 20 cm

40. The sides of a triangle are 30, 70 and 80 units. If an altitude is droped upon the side of length 80 units, the larger segment cut off on this side is______.

41. In Fig., ABC is an isosceles triangle right angled at C with AC = 4 cm. Find the length of AB.