CBSE Class 10 Mathematics Triangles MCQs

Question: If ABC is a triangle right-angled at B and M, N are the mid-points of AB and BC respectively, then 4(AN2 +CM2) is equal to
a) 5AC2
b) 6AC2
c) 4AC2
d) None of these

Answer: 5AC2

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) 8.8 cm
b) 9.9 cm
c) 3.3 cm
d) 2.2 cm

Answer: 8.8 cm

Question: If ABC and DEF are similar triangles such that ∠A = 45° and ∠F = 56°, then ∠C is equal to 
a) 79°
b) 101°
c) 56°
d) 45°

Answer: 79°

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) 4 : 1
b) 1 : 4
c) 1 : 2
d) 2 : 1

Answer: 4 : 1

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: 20 cm

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) 8 cm
b) 6 cm
c) 7 cm
d) 9 cm

Answer: 8 cm

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: 100 m

Question: In an equilateral triangle ABC. If AD ⊥ BC, then
a) 3 AB2 = 4AD2
b) 3 AB2 = 2AD2
c) 4 AB2 = 3AD2
d) None of these

Answer: 3 AB2 = 4AD2

Question: In a ΔABC, 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) 4 : 21
b) 3 : 5
c) 9 : 25
d) 3 : 4

Answer: 4 : 21

Question: If E is a point on side CA of an equilateral triangle ABC such that BE ⊥ CA, then AB² + BC² + CA² is equal to
a) 4 BE2
b) 3 BE2
c) 6 BE2
d) 2 BE2

Answer: 4 BE2

Question: A square and a rhombus are always
a) neither similar nor congruent
b) congruent
c) similar
d) similar but not congruent

Answer: neither similar nor congruent

Question: The length of each side of a rhombus whose diagonals are of lengths 10 cm and 24 cm is
a) 13 cm
b) 26 cm
c) 34 cm
d) 25 cm

Answer: 13 cm

Question: In ΔABC, D and E are points on sides AB and AC respectively such that DE||BC and AD:DB = 2 : 3. If EA = 6 cm, then AC is equal to
a) 15 cm
b) 4 cm
c) 10 cm
d) 9 cm

Answer: 15 cm

Question: AD is the bisector of ∠BAC in ΔABC. If AB = 10cm, AC = 6cm and BC = 12cm then BD is equal to
a) 7.5 cm
b) 5.6 cm
c) 6.5 cm
d) 5 cm

Answer: 7.5 cm

Question: D and E are respectively the points on the sides AB and AC of a triangle ABC such that AE = 5 cm, AC = 7.5 cm, DE = 4.2 cm and DE||BC. Then length of BC is equal to
a) 6.3 cm
b) 8.4 cm
c) 2.1 cm
d) 10.5 cm

Answer: 6.3 cm

Question: The area of two similar triangles are respectively 25 cm2 and 81 cm2. The ratio of their corresponding sides is
a) 5 : 9
b) 5 : 4
c) 9 : 5
d) 10 : 9

Answer: 5 : 9

Question: If ΔABC and ΔDEF are similar such that 2AB =DE and BC = 8 cm, then EF is equal to
a) 16 cm
b) 12 cm
c) 8 cm
d) 4 cm

Answer: 16 cm

Question: The lengths of the diagonals of a rhombus are 18 cm and 24 cm. Then the length of the side of the rhombus is
a) 15 cm
b) 30 cm
c) 28 cm
d) 26 cm

Answer: 15 cm

Question: XY is drawn parallel to the base BC of a ΔABC cutting AB at X and AC at Y. If AB = 4BX and YC = 2cm, then AY is equal to
a) 6 cm
b) 8 cm
c) 4 cm
d) 2 cm

Answer: 6 cm

Question: Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If distance between their foot is 12m, the distance between their tops is
a) 13 m
b) 14 m
c) 11 m
d) 12 m

Answer: 13 m

Question: In a ABC right - angled at A, AB = 5cm and AC = 12cm. If AD ⊥ BC, then AD is equal to
a) 60/13 cm
b) 13/60 cm
c) 13/2 cm
d) None of these

Answer: 60/13 cm

Question: If ABC is an equilateral triangle such that AD⊥BC, then AD² is equal to
a) 3CD2
b) 4CD2
c) 2CD2
d) 1CD2

Answer: 3CD2

Question: In ΔLMN and ΔPQR, ∠L = ∠P, ∠N = ∠R and MN = 2QR. Then the two triangles are
a) similar but not congruent
b) congruent as well as similar
c) congruent but not similar
d) neither congruent nor similar

Answer: similar but not congruent

Question: Two circles are always
a) similar but may not be congruent
b) none of these
c) congruent
d) neither similar nor congruent

Answer: similar but may not be congruent

Question : Given that ΔABC~ΔDEF . If DE= 2AB and BC= 3cm then, EF is equal to ___________.
(a) 12cm
(b) 2cm
(c) 1.5cm
(d) 6cm

Answer : D

Question : The straight line distance between A and B is (see the Fig.1):

(a) 5√3
(b) 5
(c) 3√5
(d) 5√/2

Answer : C

Question : In a triangle ABC, ∠A=25°, ∠B = 35° and AB = 16units. In triangle PQR, ∠P = 35°, ∠Q=120° and PR-4 units. Which of the following is true?
(a) ar(Δ ABC) = 2ar(Δ PQR)
(b) ar(Δ ABC) = 4ar(Δ PQR)
(c) ar(Δ ABC) = 8ar(Δ PQR)
(d) ar(Δ ABC) = 16ar(Δ PQR)

Answer : B

Question : The altitude of an equilateral triangle, having the length of its side as 12cm, is: 
(a) 6√2 cm
(b) 6cm
(c) 8.5cm
(d) 6√3 cm

Answer : D

Question : The areas of two similar triangles are 49cm² and 64cm² respectively. The ratio of their corresponding sides is
(a) 49:64
(b) 7:8
(c) 64:49
(d) None of these

Answer : B

Question : If ΔABC is similar to ΔDEF such that BC =3cm, EF=4cm and area of ΔABC=54cm². The area of ΔDEF is:
(a) 106cm²
(b) 96cm²
(c) 120cm²
(d) 132cm²

Answer : B

Question : All the equilateral triangles are ________________.
(a) Similar
(b) Congruent
(c) Both (a) and (b)
(d) None

Answer : A

Question : A triangle PQR is similar to another triangle ABC such that ar(PQR)=4ar(ABC). The ratio of their perimeters is given as:
(a) 2:1
(b) 1:2
(c) 4:1
(d) None of these

Answer : A

Question : In a right triangle ABC right angled at C, AC=BC. Then AB²= ___ × AC².
(a) 1
(b) 2
(c) 4
(d) None of these

Answer : B

Question : If the three sides of a triangle are a , 3a , 2a then the measure of the angle opposite to the longest side is:
(a) 60^o
(b) 90^o
(c) 45^o
(d) 30^o

Answer : B

Question : QA and PB are perpendicular on AB, if AO = 10cm, BO=6cm and PB=9cm, then measure of AQ (see the Fig.2):

 

(a) 15cm
(b) 25cm
(c) 10cm
(d) None of these

Answer : A

Question : In right triangles ABD and BDC (see the figure given in Fig.3), AB = x and CD=y, then PQ is:
(a) xy/(x+y)
(b) (x–y)/xy
(c) (x+y)/xy
(d) None of these

Answer : A

Question : In the figure (see the Fig.4) FGH and PQR are two triangles. If the measurements are as shown in the figure, then PR is equal to:
(a) 16cm
b) 12cm
(c) 8cm
(d) 4cm

Answer : C

Question : If ΔABC ~ ΔPQR , ar(PQR)=100cm² and AB/PQ= 1/2 then, ar(ABC) is:
(a) 50cm²
(b) 25cm²
(c) 4cm²
(d) None of these

Answer : B

Question : The areas of two similar triangles are 144cm² and 81cm². If one median of the first triangle is 16cm, length of corresponding median of the second triangle is:
(a) 9cm
(b) 27cm
c) 12cm
(d) 16cm

Answer : C

Question : In the given figure, x is

(A) 𝑎𝑏/𝑎+𝑏
(B) 𝑎𝑐/𝑏+𝑐
(C) 𝑏𝑐/𝑏+𝑐
(D) 𝑎𝑐/𝑎+𝑐
Answer : B

Question : If Δ𝐴𝐵𝐶~Δ𝐸𝐷𝐹 and Δ𝐴𝐵𝐶 is not similar to Δ𝐷𝐸𝐹, then which of the following is not true?
(A) 𝐵𝐶×𝐸𝐹=𝐴𝐶×𝐹𝐷
(B) 𝐴𝐵×𝐸𝐹=𝐴𝐶×𝐷𝐸
(C) 𝐵𝐶×𝐷𝐸=𝐴𝐵×𝐸𝐹
(D) 𝐵𝐶×𝐷𝐸=𝐴𝐵×𝐹𝐷
Answer : A

Question : The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is .
(A) 5.4 cm
(B) 6.8 cm
(C) 2.5 cm
(D) 4 cm
Answer : A

Question : D and E are respectively the points on sides AB and AC of triangle ABC such that AB=3cm, BD = 1.5cm, BC = 7.5cm and 𝐷𝐸∥𝐵𝐶. Then length of DE is
(A) 2cm
(B) 2.5 cm
(C) 3.75 cm
(D) 3cm
Answer : B

Question : Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the length of shadow of smaller pole is 12 m, then length of shadow of bigger pole.
(A) 22 m
(B) 14 m
(C) 13 m
(D) 11 m
Answer : A

Question : D and E are points on the sides AB and AC respectively of a ΔABC such that DE ∥ BC. Find the value of x when AD = x cm, DB = (x − 2) cm, AE = (x + 2) cm and EC = (x − 1) cm.
(A) 2 cm
(B) 3 cm
(C) 4 cm
(D) none of the above
Answer : C

Question : In the given figure, 𝐷𝐸∥𝐵𝐶 . The value of EC is

(A) 1.5cm
(B) 3cm
(C) 2cm
(D) 1cm
Answer : C

Question : In ΔABC, DE || BC and AD = 4cm, AB = 9cm. AC = 13.5 cm then the value of EC is

(A) 6 cm
(B) 7.5 cm
(C) 9 cm
(D) none of these
Answer : B

Question : It is given that, Δ𝐴𝐵𝐶~Δ𝐸𝐷𝐹 such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm then the sum of the remaining sides of the triangles is
(A) 23.05 cm
(B) 16.8 cm
(C) 6.25 cm
(D) 24 cm
Answer : A

Question : If ΔABC and ΔDEF are similar triangles such that ∠A = 57° and ∠E = 83°.
Find ∠C.
(A) 33⁰
(B) 30⁰
(C) 40⁰
(D) 83⁰
Answer : C

Question : The ratio of the areas of two similar triangles is equal to the:
(a) ratio of their corresponding sides
(b) ratio of their corresponding altitudes
(c) ratio of the squares of their perimeters
(d) ratio of the squares of their corresponding sides

Answer : D

 

Question. A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, then the length of her shadow after 4 seconds.
(a) 1.2 m
(b) 1.6 m
(c) 2 m
(d) none of these

Question. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
(a) 42 m
(b) 48 m
(c) 54 m
(d) none of these

Question. ΔABC ~  ΔDEF and their areas be, respectively, 64 cm² and 121 cm². If EF = 15.4 cm, the value of BC is. 
(a) 11.2 cm
(b) 15.4 cm
(c) 6.4 cm
(d) none of these

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

Question. Areas of two similar triangles are in the ratio 4 : 9. Sides of these triangles are in the ratio
(a) 2 : 3
(b) 4 : 9
(c) 81 : 16
(d) 16 : 81

Question. If in triangle ABC and DEF, AB/DE = BC/FD, then they will be similar when
(a) ∠B = ∠E
(b) ∠A = ∠D
(c) ∠B = ∠D
(d) ∠A = ∠F

Question. It is given that ΔABC∼ΔPQR with BC/QR = 1/3 , , then ar(ΔABC)/ar(ΔPQR) is equal to
(a) 9 
(b) 3
(c) 1/3
(d) 1/9

Question. If is given that ΔABC - ΔPQR, with BC/QR = 1/3, then ar(ΔABC)/ar(ΔPQR) is equal to
(a) 9
(b) 3
(c) 1/3
(d) 1/r

Question. In ΔABC, DE || BC and AD = 4cm, AB = 9cm. AC = 13.5 cm then the value of EC is

(a) 6 cm
(b) 7.5 cm
(c) 9 cm
(d) none of these

Question. In figure DE || BC then the value of AD is
(a) 2 cm
(b) 2.4 cm
(c) 3 cm
(d) none of the above

Question. ABC and BDE are two equilateral triangles such that BD (2/3) BC . The ratio of the areas of triangles ABC and BDE are
(a) 2 : 3
(b) 3 : 2
(c) 4 : 9
(d) 9 : 4

Question. A ladder is placed against a wall such that its foot is at distance of 2.5 m from the wall and its topreaches a window 6 m above the ground. The length of the ladder is
(a) 6.5 m
(b) 7.5 m
(c) 8.5 m
(d) 9.5 m

Question. If the corresponding sides of two similar triangles are in the ratio 4 : 9, then the areas of these triangles are in the ratio is
(a) 2 : 3
(b) 3 : 2
(c) 81 : 16
(d) 16 : 81

Question. IfΔABC ~ ΔPQR , BC = 8 cm and QR = 6 cm, the ratio of the areas of ΔABC and ΔPQR is
(a) 8 : 6
(b) 6 : 8
(c) 64 : 36
(d) 9 : 16

Question. IfΔABC ~ ΔPQR , area of ΔABC = 81cm2, area of ΔPQR = 144cm2 and QR = 6 cm, then length of BC is
(a) 4 cm
(b) 4.5 cm
(c) 9 cm
(d) 12 cm

Question. Sides of triangles are given below. Which of these is a right triangle?
(a) 7 cm, 5 cm, 24 cm
(b) 34 cm, 30 cm, 16 cm
(c) 4 cm, 3 cm, 7 cm
(d) 8 cm, 12 cm, 14 cm

Question. If a ladder 10 m long reaches a window 8 m above the ground, then the distance of the foot of the ladder from the base of the wall is
(a) 18 m
(b) 8 m
(c) 6 m
(d) 4 m

Question. A girl walks 200 towards East and the she walks 150m towards North. The distance of the girl from the starting point is
(a) 350m
(b) 250m
(c) 300m
(d) 225m 

Question : A vertical pole of length 20 m casts a shadow 10 m long on the ground and at the same time a tower casts a shadow 50 m long, then the height of the tower.
(a) 100 m
(b) 120 m
(c) 25 m
(d) none of these

Question : The areas of two similar triangles are in the ratio 4 : 9. The corresponding sides of these triangles are in the ratio
(a) 2 : 3
(b) 4 : 9
(c) 81 : 16
(d) 16 : 81

Question : The areas of two similar triangles ΔABC and  ΔDEF are 144 cm² and 81 cm², respectively. If the longest side of larger  ΔABC be 36 cm, then the longest side of the similar triangle  ΔDEF is
(a) 20 cm
(b) 26 cm
(c) 27 cm
(d) 30 cm

Question : The areas of two similar triangles are in respectively 9 cm2 and 16 cm2. The ratio of their corresponding sides is
(a) 2 : 3
(b) 3 : 4
(c) 4 : 3
(d) 4 : 5

Question : Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of their corresponding heights is
(a) 3 : 2
(b) 5 : 4
(c) 5 : 7
(d) 4 : 5

Question : If  ΔABC and  ΔDEF are similar such that 2AB = DE and BC = 8 cm, then EF =
(a) 16 cm
(b) 112 cm
(c) 8 cm
(d) 4 cm

Question : XY is drawn parallel to the base BC of a  ΔABC cutting AB at X and AC at Y. If AB = 4BX and YC = 2 cm, then AY =
(a) 2 cm
(b) 6 cm
(c) 8 cm
(d) 4 cm

Question : Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, the distance between their tops is
(a) 14 cm
(b) 12 cm
(c) 13 cm
(d) 11 cm

Question : If D, E, F are midpoints of sides BC, CA and AB respectively of  ΔABC , then the ratio of the areas of triangles DEF and ABC is
(a) 2 : 3
(b) 1 : 4
(c) 1 : 2
(d) 4 : 5

Question : If  ΔABC and  ΔDEF are two triangles such that

(a) 2 : 5
(b) 4 : 25
(c) 4 : 15
(d) 8 : 125

Question : In triangles ABC and DEF, °, AB : ED = AC : EF and °, then ΔB =
(a) 35° 
(b) 65° 
(c) 75° 
(d) 85°

Question : If ABC and DEF are similar triangles such that °, then
(a) 50°
(b) 60°
(c) 70°
(d) 80°