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Please refer to the MCQ Questions for Class 10 Triangles Maths Chapter 6 with Answers. The following Triangles Class 10 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 10. Our experts have designed MCQ Questions for Class 10 Triangles with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 10 Mathematics

## Triangles Class 10 MCQ Questions with Answers

See below Triangles Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question.. In ΔPQR, L and M are points on sides PQ and PR respectively such that PL:LQ =1:3. If MR = 6.6 cm, then PR is equal to**(a) 2.2 cm

(b) 3.3 cm

(c) 8.8 cm

(d) 9.9 cm

**Answer**

c

** Question.**. The area of two similar triangles DPQR and DXYZ are 144 cm2 and 49 cm2 respectively. If the shortest side of larger ΔPQR be 24 cm, then the shortest side of the smaller triangle ΔXYZ is

(a) 7 cm

(b) 14 cm

(c) 16 cm

(d) 10 cm

**Answer**

B

** Question.**. If ABC and DEF are two triangles such that AB/EF = BC/FD = CA/DE = 3/4, then ar (ΔDEF) : ar (ΔABC)

(a) 3 : 4

(b) 4 : 3

(c) 9 : 16

(d) 16 : 9

**Answer**

D

** Question.**. The lengths of the diagonals of a rhombus are 24 cm and 32 cm. Then, the length of the side of the rhombus is

(a) 20 cm

(b) 10 cm

(c) 40 cm

(d) 30 cm

**Answer**

A

** Question.**. If in two triangles ABC and PQR, AB/RQ=BC/QP=CA/PR , then

(a) ΔABC~ΔPRQ

(b) ΔCBA ~ΔPQR

(c) ΔPQR ~ΔACB

(d) ΔACB~ΔRQP

**Answer**

B

** Question.**. In Fig. 4.50, two line segments AC and BD intersect each other at the point P such that AP = 8 cm, PB = 4 cm, PC = 3 cm and PD = 6 cm. If ÐAPB = 50° and ΔCDP = 30°, then ÐPBA is equal to

(a) 50°

(b) 30°

(c) 60°

(d) 100°

**Answer**

D

**Question.. If DABC~ΔRPQ, ar( ΔABC)/( ΔPQR ) = 16/9, AB= 20 cm and AC = 12 cm, then PR is equal to**

(a) 15 cm

(b) 9 cm

(c) 45/4cm

(d) 27/4cm

**Answer**

A

**Question.. A square and a rhombus are always **

(a) similar

(b) congruent

(c) similar but not congruent

(d) neither similar nor congruent

**Answer**

D

**Question.. If DABC is not similar to DDEF under the correspondence ABC « DEF, then which of the following is surely not true?**

(a) BC.EF = AC.FD

(b) AB.EF = AC.DE

(c) BC.DE = AB. EF

(d) BC.DE = AB.FD

**Answer**

C

**Question.. In ΔLMN and ΔPQR, ∠L =∠P , ∠N =∠R and MN = 2QR. Then the two triangles are **

(a) congruent but not similar

(b) similar but not congruent

(c) neither congruent nor similar

(d) congruent as well as similar

**Answer**

B

**Question.. In ΔABC, if AB= 6√3 cm, AC =12 cm and BC = 6 cm, then ∠B is **

(a) 120°

(b) 60°

(c) 90°

(d) 45°

**Answer**

C

**Question.. Two circles are always **

(a) congruent

(b) neither similar nor congruent

(c) similar but may not be congruent

(d) none of these

**Answer**

C

**Question.. 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

**Answer**

A

**Question.. If ΔPRQ ~ ΔXYZ, then **

(a) PR/XZ=RQ/YZ

(b)PQ/XY=PR/XZ=

(c)PQ/XZ=QR/YZ

(d)QR/XZ=PR/XY

**Answer**

C

**Question.. The length of each side of a rhombus whose diagonals are of lengths 10 cm and 24 cm is **

(a) 25 cm

(b) 13 cm

(c) 26 cm

(d) 34 cm

**Answer**

B

**Question.. ΔABC and ΔBDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is **

(a) 2 : 1

(b) 1 : 2

(c) 1 : 4

(d) 4 : 1

**Answer**

D

**Question.. If in two triangles ABC and PQR, AB/QR=BC/PR=CA/PQ , then **

(a) ΔPQR ~ ΔCAB

(b) ΔPQR ~ ΔABC

(c) ΔCBA ~ΔPQR

(d) ΔBCA ~ ΔPQR

**Answer**

A

**Question.. If in triangles ABC and XYZ, ∠B= ∠X and ∠C = ∠Z, then which of the following is not true? **

(a) AB/XY=BC/YZ

(b) AB/YX=BC/XZ

(c) BC/XZ=CA/YZ

(d) CA/ZY=AB/XY

**Answer**

A

**Question.. In Δ ABC and Δ RPQ, AB= 4 5 . cm, BC = 5cm, CA= 6 2 cm, PR=12 2 cm, PQ =10cm, QR = 9cm. If ∠A= 75° and ∠B= 55°, then ∠P is equal to **

(a) 75°

(b) 55°

(c) 50°

(d) 130°

**Answer**

C

**Question.. If in triangles ΔABC and ΔDEF, AB/EF=AC/DE , then they will be similar when **

(a) ∠A= ∠D

(b) ∠A= ∠E

(c) ∠B= ∠E

(d) ∠C = ∠F

**Answer**

B

**Question.. It is given that ar (ΔABC) = 81 square units and ar (ΔDEF)= 64 square units. If DABC ~ DDEF, then **

(a) AB/DE= 81/64

(b) AB2/DE2 =9/8

(c) AB/DE= 9/8

(d) AB = 81 units, DE = 64 units

**Answer**

C

**Question.. If ΔPQR ~ ΔXYZ and PQ/XY= 5/2, then ar( ΔXYZ )/( ΔPQR ) is equal to **

(a) 4/25

(b) 2/5

(c) 25/4

(d) 5/2

**Answer**

A

** Question.**. If ABC and DEF are similar triangles such that ∠A = 45° and ÐF = 56°, then ∠C is equal to

(a) 45°

(b) 56°

(c) 101°

(d) 79°

**Answer**

D

** Question.**. ΔABC and ΔBDE are two equilateral triangles such that D is the mid-point of BC. The ratio of the areas of triangles ABC and BDE is

(a) 2 : 1

(b) 4 : 1

(c) 1 : 4

(d) 1 : 2

**Answer**

B

**Question. In a DABC, points D and E lie on the sides AB and AC respectively, such that BCED is a trapezium. If DE:BC = 2:5, then ar (ADE):ar (BCED) **

(a) 3 : 4

(b) 4 : 21

(c) 3 : 5

(d) 9 : 25

**Answer**

B

**Question. If E is a point on side CA of an equilateral triangle ABC such that BE ^CA, then AB ^{2} + BC^{2} +CA^{2} is equal to **

(a) 2 BE

^{2}

(b) 3 BE

^{2}

(c) 4 BBE

^{2}

(d) 6 BE

^{2}

**Answer**

C

**Question. In trapezium ABCD with AB||CD, the diagonals AC and BD intersect at O. If AB= 5 cm and AO/OC=OB/DO = 1/2, then DC is equal to **

(a) 12 cm

(b) 15 cm

(c) 10 cm

(d) 20 cm

**Answer**

C

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

(a) 10 cm

(b) 14 cm

(c) 30 cm

(d) 25 cm

**Answer**

C

**Question. A vertical stick 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. The height of the tower is **

(a) 100 m

(b) 120 m

(c) 25 m

(d) 200 m

**Answer**

A

**Question. The areas of two similar triangles are 81 cm ^{2} and 49 cm^{2} respectively. If the altitude of the bigger triangle is 4.5 cm, find the corresponding altitude of the smaller triangle. **

(a) 3 cm

(b) 2.5 cm

(c) 4 cm

(d) 3.5 cm

**Answer**

D

**Question. In trapezium ABCD, AB||CD. If OA= x – 4 , OB = 3x – 19,OC = 4 and OD = x – 3 , find ‘x’. **

(a) 10 units

(b) 9 units

(c) 12 units

(d) 8 units

**Answer**

D

**Question. The side of an equilateral triangle is 10 cm. What is its altitude? **

(a) 5 2cm

(b) 5 3cm

(c) 12cm

(d) 5cm

**Answer**

B

**Question. In the given figure, ΔABE~ΔDCE. **

**Find the difference between ∠ABE and ∠AEB.**

(a) 130°

(b) 15°

(c) 35°

(d) 115°

**Answer**

D

**Question. At what height does the tip of a 34m long ladder placed at a distance of 16 m from a wall, touch the wall? **

(a) 29 m

(b) 34 m

(c) 30m

(d)18 m

**Answer**

C

**Question. Identify the incorrect statement. **

(a) A right angled triangle may have 1,1 and 2 as its sides.

(b) 1,2, √3 are the sides of a right angled triangle.

(c) The ratio of corresponding sides of two squares whose areas are in the ratio 4:1 is 2 :1.

(d) 17,8 and 15 are the sides of a right angled triangle.

**Answer**

A

**Question. At some point of time on a summer evening, an 8 m tall flag post casts a 15 m long shadow. What is the distance between the tips of the flag post and its image? **

(a) 15m

(b) 28m

(c) 23m

(d) 17m

**Answer**

D

**Question. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. What is the length of the side of the rhombus? **

(a) 9cm

(b) 10cm

(c) 8 cm

(d) 20 cm

**Answer**

B

**Question. In ΔABC , D is a point on AB and E is a point on BC such that DE| |AC and area of ΔDBE = 1/2 area of ΔABC. Find AD/AB . **

(a) 1 – √2/2

(b) √2 -1/√2

(c) √2 – 1/2

(d) √2 + 1/2

**Answer**

B

**Question. Given xy = 4cm , QR = 8 cm and area of ΔPXY = 25sq.cm, what is the area of ΔPQR ? **

(a) 49 cm^{2}

(b) 81 cm^{2}

(c) 64 cm^{2}

(d) 100 cm^{2}

**Answer**

D

**Question. In an equilateral triangle ABC, if AD^BC, then **

(a) 2 AB^{2} = 3AD^{2}

(b) 4 AB^{2} = 3AD^{2}

(c) 3 AB^{2} = 4AD^{2}

(d) 3 AB^{2} = 2AD^{2}

**Answer**

C

**Question. If ABC is an isosceles triangle and D is a point on BC such that AD^BC, then **

(a) AB2 – AD2 = BD.DC

(b) AB2 – AD2 = BD^{2} – DC^{2}

(c) AB2 + AD^{2} = BD.DC

(d) AB2 + AD2 = BD^{2} – DC^{2}

**Answer**

A

**Question.Two poles of height 9 m and 15 m stand vertically upright on a plain ground. If the distance between their tops is 10m, the distance between their foot is **

(a) 9 cm

(b) 7 cm

(c) 8 cm

(d) 6 cm

**Answer**

C

**Question. In the given figure, if AD⊥ BC, then AB ^{2}+ CD^{2} equals **

(a) AD

^{2}+ BC

^{2}

(b) AD

^{2}+ CD

^{2}

(c) BD

^{2}+ AC

^{2}

(d) none of them

**Answer**

C

**Question. The areas of two similar triangles are 144 cm2 and 81 cm2. If one median of the first triangle is 16 cm, length of corresponding median of the second triangle is **

(a) 9 cm

(b) 27 cm

(c) 12 cm

(d) 16 cm

**Answer**

C

**Question. O is a point on side PQ of a DPQR such that PO = QO = RO, then which of the following is true? **

(a) RO^{2}= PR×QR

(b) PR^{2}+ QR^{2}= PQ^{2 }

(c) QR^{2}= OQ^{2}+ QR^{2}

(d) OP^{2}+ OR^{2}= PR^{2}

**Answer**

B

**Question. If in two triangles ABC and DEF, AB/DF= BC/FE=CAED then **

(a) ΔABC~ΔDEF

(b) ΔABC~ΔEDF

(c) ΔABC~ΔEFD

(d) ΔABC~ΔDFE

**Answer**

D

**Question. The areas of two similar triangles are 144 cm ^{2} and 64 cm^{2}. If one median of the first triangle is 12 cm, length of corresponding median of the second triangle is **

(a) 9 cm

(b) 8 cm

(c) 7 cm

(d) 16 cm

**Answer**

B

**Question. In DABC, if AD is the bisector of ∠A then (ar ABD)/ (ar ACD ) is equal to **

(a) AB/BC

(b) AB/AD

(c) AC/BC

(d) AB/AC

**Answer**

D

**Question. The ratio between the area of an equilateral triangle described on one diagonal of square and area of an equilateral triangle described on one side of the square is **

(a) 1 : 2

(b) 4 : 1

(c) 2 : 1

(d) 1 : 1

**Answer**

C

**Question. In figure, DE ll BC. If AD/DB= 3/2 and AE = 2.7 cm, then EC is equal to **

(a) 2.0 cm

(b) 1.8 cm

(c) 4.0 cm

(d) 2.7 cm

**Answer**

B

**Question. In an equilateral triangle ABC if AD = BC, which of the following is true? **

(a) 2AB^{2}= 3AD^{2}

(b) 4AB^{2}= 3AD^{2}

(c) 3AB^{2}= 4AD^{2}

(d) 3AB^{2}= 2AD^{2}

**Answer**

C

^{ }**Question. If DABC is an equilateral triangle such that AD = BC, then which of the following is true? **

(a) 3/2DC^{2}

(b) 2DC^{2}

(c) 3CD^{2}

(d) 4DC^{2}

**Answer**

C

**Question. Two similar figures are shown. **

**What are the values of x and y? **

(a) x = 58°, y = 130°

(b) x = 98°, y = 76°

(c) x = 82°, y = 84°

(d) x = 130°, y = 84°

**Answer**

A

**Question. Two quadrilaterals are such that their diagonals bisect each other. What additional information is required to conclude that the quadrilaterals are similar? **

(a) Opposite angles are equal

(b) Opposite sides are equal

(c) Diagonals bisect at right angle and adjacent angles are equal

(d) Diagonals are equal and opposite sides are equal

**Answer**

C

**Question. Consider the figure below. **

**Which of the following statement is correct about the triangles in the figure?**

(a) ΔAOB~ ΔDOC because AO/DO= BO/CO

(b) ΔAOB~ΔDOC because∠AOB=∠DOC

(c) ΔAOB~ ΔDOC because AO/DO= BO/CO and ∠BAO = ∠CDO

(d) ΔAOB~ ΔDOC because AO/DO= BO/CO and ∠AOB =∠DOC

**Answer**

D

**Question. Consider the figure below. **

**Which of the following statement help proving that triangle ABO is similar to triangle DOC?**

(i) ∠B = 70° and (ii) ∠C = 70°

(a) Statement (i) alone is sufficient, but statement (ii) alone is not sufficient.

(b) Statement (ii) alone is sufficient, but statement (i) alone is not sufficient.

(c) Each statement alone is sufficient.

(d) Both statement together is sufficient, but neither statement alone is sufficient.

**Answer**

C

**Question. ΔABC is a right triangle right angled at A and AD = BC . Then, BD/DC is equal to **

(a) (AB/AC)^{2}

(b) AB/AC

(c) (AB/ AD)^{2}

(d) AB/AD

**Answer**

B

**Question. In the figure below, PQ || CB. To the nearest tenth, what is the length of QB? **

(a) 1.4 cm

(b) 1.7 cm

(c) 1.8 cm

(d) 2.2 cm

**Answer**

C

**Question. Consider the triangles below. **

**Which statement is correct?**

(a) For triangles to be similar, the measure of ∠A = 40°.

(b) For triangles to be similar, the measure of ∠A = 100°.

(c) Triangles are similar as all isosceles triangles are similar.

(d) Triangles are similar as corresponding sides of the triangles are in the ratio 1 : 2.

**Answer**

B

**Question. The area of two similar triangles are a and k2a. What is the ratio of the corresponding side lengths of the triangles? **

(a) 1 : k

(b) 1 : k^{2}

(c) 1 : a

(d) 1 : a^{2}

**Answer**

A

**One Word Questions :**

**Question. In figures, name the similar triangles. **

**Answer**

ΔABC ∼ΔFDE

**Question. In figure, PQ ll MN . If KP/PM = 4/13 and QN = 26, find KQ. **

**Answer**

8

**Question. In figure, AX is the bisector of ∠BAC . If AB = 3cm, AC = 4cm and BC = 5cm, find BX. **

**Answer**

15/7

**Question. In figure, PT is bisector of ∠QPR , find TR. **

**Answer**

3.6cm

**Question. In figure, find x . **

**Answer**

10cm

**Question. ΔABC and ΔDEC are the right triangles with ∠B=∠E =90° ; find BE. **

**Answer**

15cm

**Question. In figure, find x if DE ll BC . **

**Answer**

x = 11

**Question. In a trapezium ABCD, AB ll CD and AB = 2CD. The diagonals AC and BD meet at O. If the area of ΔAOB is 84 sq.cm., find the area of ΔCOD.**

**Answer**

21 sq.cm.

**Question. In figure, find the value of x . **

**Answer**

4cm

**Question. In ΔABC , DE ll BC and AD/DB = 2/3 , find AE : AC. **

**Answer**

2 : 5

**Question. In figure, DE ll BC . If AD = 5BD and EC = 1.6cm, find AE. **

**Answer**

8cm

**Question. Select the pair of similar figures. **

**Answer**

(a) and (c)

**Question. In figure, ΔABO ∼ΔDCO. If AB = 3cm, CD = 2cm, OC = 3.8cm and OD = 3.2cm, find OA. **

**Answer**

4.8cm

**Question. In figures, ΔABC ∼ ΔDEF , find the value of x. **

**Answer**

8cm

**Question. In a rhombus ABCD with side 4cm, AC and BD are diagonals bisecting at O. Find the value of AC² + BD².**

**Answer**

64cm

**Question. In figure, ΔACB ∼ΔECD, find ∠B . **

**Answer**

70°

**Question. In figures, ΔABC ∼ΔDEF , find ∠F . **

**Answer**

62°

**Question. In figure, P and Q are points on the sides AB and AC respectively of ΔABC , If PQ = 4cm, find BC. **

**Answer**

12 cm

**Question. In figures, ΔABC ∼ΔDEF , find BC/EF . **

**Answer**

½

**Question. The corresponding attitude of two similar triangles are 7cm and 8cm respectively. Find the ratio of their areas.**

**Answer**

49 : 64

**Question. In ΔABC,DE ll BC . If AD = 6cm, DB = 9cm and AE = 8cm, find AC. **

**Answer**

20cm

**Question. ABC is an isosceles triangle in which ∠C =90° . If AC = 6cm, find AB².**

**Answer**

72cm

**Question. In figure, if PQ ll BC and PR ll CD , AR = 4cm, AD = 16cm and AQ = 3cm. Find AB. **

**Answer**

12cm

**Question. In figure, if AB/AC = BD/CD , then find ∠ABD. **

**Answer**

40°

**Question. In figure AB = 8cm, BC = 12cm and AE = 6cm. Find area of the rectangle BCDE. **

**Answer**

120cm²

All these MCQ Question given here are simply solved so that students can easily understand th concept and logic in each correct options.We have all the study material for Class 10 like Sample Paper, Exam Questions, NCERT Solutions, NCERT Book, and Revision notes. If you have any problem regarding this study material please write it in the comment box given below.