# MCQ Questions For Class 10 Triangles

Triangles Class 10 MCQ is one of the best strategies to prepare for the CBSE Class 10 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Triangles class 10, which will help them all through their board test.

## Triangles Class 10 MCQ Questions with Answer

Class 10 Math MCQ with answers are given here to chapter 6 Triangles. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 10 Mathematics syllabus. By Solving these Class 10 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 10 Annual exam.

Learn Triangles Class 10 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 10 Mathematics Quadratic Equation MCQ with answers given below.

Question 1. The ratio of the areas of two similar right triangles is 9 : 16. The length of one of the sides of the smaller triangle is 15 cm. How much longer is the length of the corresponding side of the larger triangle from smaller triangle?
(a) 2 cm
(b) 3 cm
(c) 4 cm
(d) 5 cm

D

Question 2. If ΔDABC ~ ΔDDEF, (ar ΔABC )/ (ar ΔDEF )= 9/25, D D = , BC = 21 cm, then EF is equal to
(a) 9 cm
(b) 6 cm
(c) 35 cm
(d) 25 cm

C

Question 3. In the figure below, PQ || BC.

The ratio of the perimeter of triangle ABC to the perimeter of triangle APQ is 3:1. Given that the numerical value of the area of triangle APQ is a whole number, which of the following could be the area of the triangle ABC?
(a) 28
(b) 60
(c) 99
(d) 120

C

Question 4. The ratio of the areas of two similar triangles, ABC and PQR shown below is 25 : 144. What is the ratio of their medians AM and PN?
(a) 5 : 12
(b) 5 : 16
(c) 12 : 5
(d) 25 : 144

A

Question 5. Observe the right triangle ABC, right angled at A as shown below. If BP ⊥ AC, then which of the following is NOT correct? B A P C
(a) ΔAPB ~ ΔABC
(b) ΔAPB ~ ΔBPC
(c) BC2 = CP . AC
(d) AC2 = AB . CB

D

Question 6. Observe the right triangle ABC, right angled at B as shown below.

What is the length of PC?
(a) 2.5 cm
(b) 4.5 cm
(c) 6 cm
(d) 7.5 cm

D

Question 7. Rohit is 6 feet tall. At an instant, his shadow is 5 feet long. At the same instant, the shadow of a pole is 30 feet long. How tall is the pole?
(a) 12 feet
(b) 24 feet
(c) 30 feet
(d) 36 feet

D

Question 8. Ankit is 5 feet tall. He places a mirror on the ground and moves until he can see the top of a building. At the instant when Ankit is 2 feet from the mirror, the building is 48 feet from the mirror. How tall is the building?
(a) 96 feet
(b) 120 feet
(c) 180 feet
(d) 240 feet

B

Question 9. Consider the following three clamis about a triangle ABC with side lengths m, n and r.
(i) ABC is a right triangle provided n2 − m2 = r2.
(ii) Triangle with side lengths m + 2, n + 2 and r + 2 is a right-angle triangle.
(iii) Triangle with side lengths 2m, 2n and 2r is a right-angle triangle.
Which of these is correct?
(a) Statement (i) would be correct if n > m, n > r and statement 2 would be correct if ABC is a right triangle.
(b) Statement (i) would be correct if r > m, r > n and statement 2 would be correct if ABC is a right triangle.
(c) Statement (i) would be correct if n > m, n > r and statement 3 would be correct if ABC is a right triangle.
(d) Statement (i) would be correct if r > m, r > n and statement 3 would be correct if ABC is a right triangle.

C

Question 10. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3 cm, BD = 5 cm, BC = 12.8 cm and DE || BC. Then length of DE (in cm) is
(a) 4.8 cm
(b) 7.6 cm
(c) 19.2 cm
(d) 2.5 cm

A

Question 11. Consider the figure below.
Mr Shah follows the below step to prove AB2 + BC2 = AC2.
(i) ΔAPB ~ ΔABC (ii) AP/AB=AB/AC = (iii) AB2 = AP . AC.
Which of these could be his next step?
(a) Prove ΔABC ~ ΔPAB
(b) Prove ΔAPB ~ ΔCPB
(c) Prove ΔBPC ~ ΔABC
(d) Prove ΔAPB ~ ΔBPC

C

Question 12. If D, E and F are mid points of sides BC, CA and AB repspectively of DABC, then the ratio of the areas of triangles DEF and ABC is
(a) 2 : 3
(b) 1 : 4
(c) 1 : 2
(d) 4 : 5

B

Question 13. In figure, ABC is an isosceles triangle, right-angled at C. Therefore

(a) AB2 = 2AC2
(b) BC2 = 2AB2
(c) AC2 = 2AB2
(d) AB2 = 4AC2

A

Question 14. In figure, ∠BAC = 90° and AD ⊥ BC. Then,
(a) BD . CD = BC2
(b) AB . AC = BC2
(c) BD . CD = AD2
(d) AB . AC = AD2

C

Question 15. From the given figure, then length of the sides AB and BD.

(a) 25 cm and 7 cm
(b) 25 cm and 17 cm
(c) 7 cm and 15 cm
(d) 18 cm and 7 cm

A

Question 16. ABCD is a parallelogram with diagonal AC. If a line XZ is drawn such that XZ ; ; AB then XC BX is equal to
(a) AY/AC
(b) DZ/AC
(c) AZ/ZD
(d) AC/AY

C

Question 17. Sum of squares of the sides of rhombus is equal to
(a) Sum of diagonals
(b) Difference of diagonals
(c) Sum of squares of diagonals
(d) none of them

C

Question 18. In ABC, AB/A=BD/DC, ∠B = 70° and ∠C = 50°. Then, ∠BAD = _______.

(a) 30°
(b) 40°
(c) 50°
(d) 45°

A

Question 19. The area of a right angled isosceles triangle whose hypotenuse is equal to 270 m is-
(a) 19000 m2
(b) 18225 m2
(c) 17256 m2
(d) 18325 m2

B

Question 20. The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, then AB =
(a) 10 cm
(b) 20 cm
(c) 25 cm
(d) 15 cm

D

Question 21. If ΔABC ~ ΔAPQ and ar (ΔAPQ) = 4 ar (ΔABC), then the ratio of BC to PQ is
(a) 2 : 1
(b) 1 : 2
(c) 1 : 4
(d) 4 : 1

B

Question 22. Consider a DPQR in which the relation QR2 + PR2 = 5 PQ2 holds. Let G be the points of intersection of medians PM and QN. Then ∠QGM is always
(a) less than 45°
(b) obtuse
(c) a right angle
(d) acute and larger than 45°

C

Whoever needs to take the CBSE Class 10 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 10 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Triangles class 10 MCQ are ready by the subject specialists themselves.

Question 23. In the given figure, DE || BC. The value of EC is

(a) 1.5 cm
(b) 3 cm
(c) 2 cm
(d) 1 cm

C

Question 24. Which of the following statement is false?
(a) All isosceles triangles are similar.
(b) All quadrilateral triangles are similar.
(c) All circles are similar.
(d) None of the above

A

Question 25. The length of the side of a square whose diagonal is 16 cm, is
(a) 8√ 2 cm
(b) 2√ 8 cm
(c) 4 √2 cm
(d) 2 √2 cm

A

Question 26. The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, then the length of QR is
(a) 4 cm
(b) 4.5 cm
(c) 3 cm
(d) 6 cm

D

Question 27. If ΔABC ~ ΔDEF such that BC = 2.1cm and EF = 2.8 cm. If the area of triangle DEF is 16 cm2, then the area of triangle ABC (in sq. cm) is
(a) 9
(b) 12
(c) 8
(d) 13

A

Question 28. Two isosceles triangles have their corresponding angles equal and their areas are in the ratio 25 : 36. The ratio of their corresponding height is
(a) 25 : 35
(b) 36 : 25
(c) 5 : 6
(d) 6 : 5

C

Question 29. Let P be an interior point of a DABC. Let Q and R be the reflections of P in AB and AC, respectively. If Q, A, R are collinear, then ∠A equals
(a) 30°
(b) 60°
(c) 90°
(d) 120°

C

Question 30. ΔABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Ratio between the areas of ΔABE and ΔACD is
(a) 1 : 4
(b) 2 : 1
(c) 1 : 2
(d) 4 : 3

C

Question 31. In the figure, ABC is a triangle in which AD bisects ∠A, AC = BC, ∠B = 72° and CD = 1cm. Length of BD (in cm) is

(a) 1
(b) 1 /2
(c) √5 –1 /2
(d) √3 + 1/2

C

Question 32. In a triangle ABC, ∠BAC = 90°; AD is the altitude from A on to BC. Draw DE perpendicular to AC and DF perpendicular to AB. Suppose AB = 15 and BC = 25. Then the length of EF is
(a) 12
(b) 10
(c) 5 √3
(d) 5√ 5

A

Question 33. The areas of two similar triangles are 81 cm2 and 49 cm2 respectively, then the ratio of their corresponding medians is
(a) 7 : 9
(b) 9 : 81
(c) 9 : 7
(d) 81 : 7

C

Question 34. The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the side BC. Then

(a) EF/ FA= FB / AB
(b) DF × EF = FB × FA
(c) DF × EF = (FB)2
(d) None of these

A

Question 35. ΔABC is an equilateral triangle with each side of length 2p. If AD ⊥ BC, then the value of AD is
(a) √3
(b) √3 p
(c) 2p
(d) 4p

B

Question 36. In a right angled triangle ΔABC, length of two sides are 8cm and 6cm, then which among the given statements is/ are correct?

(a) Length of greatest side is 10cm
(b) ∠ACB = 45°
(c) ∠BAC = 45°
(d) Pythagoras theorem is not applicable here.

A

Question 37. If ΔABC is an equilateral triangle such that AD ⊥ BC, then AD2 = A. 3a2/4 B. 3a2/2 C.3/4BC2 D.√3/2a
(a) A and C
(b) A
(c) D
(d) B and C

A

Question 38. Let D be a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. If AC = 21 cm, then the side of an equilateral triangle whose area is equal to the area of the rectangle with sides BC and DC is
(a) 14 × 31/2
(b) 42 × 3–1/2
(c) 14 × 33/4
(d) 42 × 31/2

C

Question 39. In ΔABC, AB = AC, P and Q are points on AC and AB respectively such that BC = BP = PQ = AQ. Then, ∠AQP is equal to (use p =180º)
(a) 2π /7
(b) 3π/7
(c) 4π/7
(d) 5π/7

D

Question 40. Let ABC be a triangle and M be a point on side AC closer to vertex C than A. Let N be a point on side AB such that MN is parallel to BC and let P be a point on side BC such that MP is parallel to AB. If the area of the quadrilateral BNMP is equal to 5/18 of the area of DABC, then the ratio AM/MC equals
(a) 5
(b) 6
(c) 18/ 5
(d) 15/ 2

A

Question 41. Which among the following is/are correct?
(a) The ratios of the areas of two similar triangles is equal to the ratio of their corresponding sides.
(b) The areas of two similar triangles are in the ratio of the corresponding altitudes.
(c) The ratio of area of two similar triangles are in the ratio of the corresponding medians.
(d) If the areas of two similar triangles are equal, then the triangles are congruent.

D

Match the following

Question 1. In figure, the line segment XY is parallel to the side AC of ΔABC and it divides the triangle into two parts of equal areas, then,

(A) → p; (B) → q; (C) → r; (D) → s

Question 2. If in a Δ ABC, DE || BC and intersects AB in D and AC in E, then.

(A) → q; (B) → p; (C) → s; (D) → r

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