MCQs for Mathematics Class 10 with Answers Chapter 6 Triangles

Students of class 10 Mathematics should refer to MCQ Questions Class 10 Mathematics Triangles with answers provided here which is an important chapter in Class 10 Mathematics NCERT textbook. These MCQ for Class 10 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 10 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 10 Mathematics examination

Chapter 6 Triangles MCQ with Answers Class 10 Mathematics

MCQ Questions Class 10 Mathematics Triangles provided below have been prepared by expert teachers of grade 10. These objective questions with solutions are expected to come in the upcoming Standard 10 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2cm, 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

B

Question. D, E and F are the mid-points of the sides BC, CA and AB respectively of a ΔABC. The ratio of the areas of ΔDEF and ΔABC is :
(a) 1 : 2
(b) 2 : 1
(c) 1 : 4
(d) 4 : 1

C

Question. In an equilateral triangle ABC, if AD ⊥ BC, then:

C

Question. In triangle DEF,GH is a line parallel to EF cutting DE in G and and DF in H. If DE = 16.5, DH =5, HF = 6 then GE = ?
(a) 9
(b) 10
(c) 7.5
(d) 8

A

Question. If a triangle and a parallelogram are on the same base and between same parallels, then what is the ratio of the area of the triangle to the area of parallelogram?
(a) 1 : 2
(b) 3 : 2
(c) 1 : 3
(d) 4 : 1

A

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

C

Question. In triangle ABC ,DE || BC AD = 3 cm, DB = 8 cm AC = 22 cm. At what distance from A does theline DE cut AC?
(a) 6
(b) 4
(c) 10
(d) 5

A

Question. 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

C

Question. Two poles stand on the ground at a distance of 20m and 50 m respectively from a point A on theground, the taller pole at 30 m from smaller pole. A cable originates from the top pf the taller pole,passing on the other pole ends on a hook at point A. If the length of the cable is 100 m , how muchof it lies between the the two poles?
(a) 50m
(b) 40 m
(c) 60 m
(d) 80 m

C

Question. In triangle ABC, if AB = 6√3 cm, AC = 12 cm and BC cm, then ∠B is
(a) 120°
(b) 60°
(c) 90°
(d) 45°

C

Question. The perpendicular AD on the base BC of a ΔABC intersects BC at D so that CD =1/4.DB
(a) 3BC2 = 5 (AC2 – AB2)
(b) 3BC2 = 5 (AB2 – AC2)
(c) 5BC2 = 3 (AC2 – AB2)
(d) 5BC2 = 3 (AB2 – AC2)

B

Question. Triangle ABC is similar to triangle DEF and their areas are 64 cm 2 and 121 cm 2 respectively. IfEF = 15.4 cm, then BC = ?
(a) 11.2 cm
(b) 8 cm
(c) 11 cm
(d) 13 cm

A

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

C

Question. The ratio of the areas of two similar triangles is equal to the:
(a) square of the ratio of their corresponding sides.
(b) the ratio of their corresponding sides
(c) square of the ratio of their corresponding angles
(d) None of the above

A

Question. In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC= and EF is parallel toBC.In what ratio does EF cut AB and CD?
(a) 1:2
(b) 3:4
(c) 2:3
(d) 1:4

C

Question. In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Lengthof the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length ofthe smallest side of the triangle PQR is :
(a) 6 cm
(b) 8 cm
(c) 7 cm
(d) 10 cm

B

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

D

Question. Points P and Q on the sides AB and AC of ΔABC are such that PQ||BC, AP: PB = 2 :3 and AQ = 4 cm. What is the measure of AC?
(a) 12cm
(b) 16cm
(c) 10cm
(d) 15cm

C

Question. In the given figure, if ΔABE ≅ ΔACD , identify the correct statement.

(c) ΔDEC~ ΔABC
(d) ΔBDE ~ ΔBAE

B

Question. A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/sec. If the lamp is 3.6 m above the ground, find the length of the girls shadow after 4 seconds.
(a) 4.8m
(b) 1.2m
(c) 1.6m
(d) 3.6m

C

Question. What is the ratio of areas of two similar triangles whose corresponding sides are in the ratio 15:19?
(a) √15 : √19
(b) 15:19
(c) 225:361
(d) 125:144

C

Question. In ΔABC,DE||BC,AD = 6cm,BD = 9cm and AE = 8cm.

Find the length of AC.
(a) 20 cm
(b) 12 cm
(c) 15 cm
(d) 18 cm

A

Question. The altitudes of two similar triangles are 4 cm and 6 cm. If the area of one triangle is 36 cm2 , what is the area of the other?
(a) 16cm2
(b) 36cm2
(c) 49 cm2
(d) 25 cm2

A

Question. In the given figure, ΔRSP~ΔRPQ .Identify the true statement.

(a) RS/RQ = RP2
(b) RP x RQ = RS2
(c) RS x RQ = RP2
(d) RQ x RS = RP

C

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

A

Question. In ΔABC, ∠A = 90° , AN ⊥ BC , BC = 12 cm and AC = 5 cm. Find the ratio ar(ΔANC) : ar(ΔABC)
(a) 122 :52
(b) 32 :122
(c) 52 :122
(d) 32 :52

C

Question. The diagonals of a rhombus are 16 cm and 12 cm. What is the measure of its side?
(a) 10cm
(b) 12cm
(c) 8cm
(d) 16cm

A

Question. If ΔABC ~ ΔDEF and EF = BC, then ar(ΔABC):(ΔDEF) is
(a) 3 : 1
(b) 1 : 3
(c) 1 : 9
(d) 9 : 1

C

Question. In a rhombus if d 1 = 16 cm, d 2 = 12 cm, then the length of the side of the rhombus is
(a) 8 cm
(b) 9 cm
(c) 10 cm
(d) 12 cm

C

Question. In triangle MNS, A and B are points on the sides MN, NS respectively. AN = MN, BS= MS.Then AB is …………………. to NS :
(a) Not Perpendicular
(b) Parallel
(c) Perpendicular
(d) Not Parallel

B

Question. In the given figure, AB || CD. Then the value of x is :

(a) 8
(b) 11
(c) 8 or 11
(d) none of these

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

B

Question. D and E are respectively the points on the sides AB and AC of a ΔABC and DE || BC, such that AD = 3 cm, AB = 12 cm, AE = 4 cm, then the value of CE is :
(a) 6 cm
(b) 9 cm
(c) 12 cm
(d) 15 cm

C

Question. Two congruent triangles are actually similar triangles with the ratio of corresponding sides as.
(a) 1:2
(b) 1:1
(c) 1:3
(d) 2:

B

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

A

Question. In the given figure, PQ || DC || AB. The value of x is :

(a) 1
(b) 2
(c) 3
(d) 4

B

Question. A vertical stick 12 m long casts a shadow 8 m long on the ground. At the same time a tower casts the shadow 40 m long on the ground. The height of the tower is :
(a) 50 m
(b) 60 m
(c) 80 m
(d) none of these

B

Question. In the given figure, <BAC = <ADB= 90°. The length of DC is :

(a) 2 cm
(b) 2.25 cm
(c) 2.5 cm
(d) 2.75 cm

B

Question. The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, the length of QR is:
(a) 5 cm
(b) 5.5 cm
(c) 6 cm
(d) none of these

C

Question. The areas of two similar triangles are 81 cm2 and 49 cm2 respectively. If the altitude of the bigger triangle is 4.5 cm, the length of corresponding altitude of smaller triangle is :
(a) 3 cm
(b) 4 cm
(c) 3.5 cm
(d) 4.5 cm

C

Question. Which geometric figures are always similar?
(a) Circles
(b) Circles and all regular polygons
(c) Circles and triangles
(d) Regular

B

Question. ΔABC ~ ΔPQR, ∠B = 50° and ∠C = 70° then ∠P is equal to
(a) 50°
(b) 60°
(c) 40°
(d) 70°

B

Question. Two isosceles triangles have equal vertex angles and their areas are in the ratio 9 : 16. The ratio of their corresponding altitudes is :
(a) 3 : 4
(b) 9 : 16
(c) 81 : 256
(d) none of these

A

Question. In the given figure, DE || BC and AD : DB = 4 : 5. Then the value of ar (ΔDEF) /ar (ΔBCF) is :

(a) 4 : 5
(b) 4 : 9
(c) 16 : 81
(d) none of these

C

Question. Two vertical poles are 24 m apart. If the heights of the poles be 17 m and 27 m; the distance between the tips of the poles is :
(a) 20 m
(b) 26 m
(c) 28 m
(d) none of these

B

Question. The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 8 cm, then the value of AB is :
(a) 12 cm
(b) 15 cm
(c) 18 cm
(d) none of these

A

Question. Each side of a rhombus is 13 cm. If one of the diagonals is 24 cm, the length of the other diagonal is :
(a) 5 cm
(b) 8 cm
(c) 10 cm
(d) 12 cm

C

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

B

Question. The area of a right-angled triangle is 60 cm2. If the larger side of the triangle exceeds the smaller side by 7 cm, the length of hypotenuse is :
(a) 10 cm
(b) 12 cm
(c) 15 cm
(d) 17 cm

D

Question. In the given figure, DE || BC, BE || XC and AD /DB = 1/2, then the value of AX/XB is:

(a) 2 : 1
(b) 3 : 1
(c) 3 : 2
(d) none of these

B

Question. In the given figure, the value of AD is :

(a) 25 cm
(b) 15 cm
(c) 30 cm
(d) none of these

B

Question. In the given figure, ΔACB ~ ΔAPQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm, AP = 2.8 cm, the value of AC is:

(a) 5.6 cm
(b) 2.8 cm
(c) 8 cm
(d) none of these

A

Question. In the given figure, express x in terms of a, b and c.

(a) x=ab/a+b
(b) x =ac/b+c
(c) x =bc/b+c
(d) x =ac/a+c

B

Question. In the given figure, P and Q are points on the sides AB and AC respectively of a triangle ABC. PQ is parallel to BC and divides the triangle ABC into 2 parts, equal in area. The ratio of PA : AB =

(a) 1 : 1
(b) ( √2 −1) : √2
(c) 1:√ 2
(d) (√ 2 −1) :1

C

Question. ABC is an isosceles triangle in which AB = AC = 10 cm, BC = 12 cm. PQRS is a rectangle inside the isosceles triangle. Given PQ = SR = y cm and PS = QR = 2x cm, then x =
(a) 6 -3y/4
(b) 6 + 6y
(c) 6 +4y/3
(d) 7x+8y/4

A

Question. Two triangles are similar if
(a) their corresponding angles are equal.
(b) their corresponding sides are equal.
(c) both are right triangle.
(d) None of the above

A

Question. The area of a right angled triangle is 40 sq. cm. and its perimeter is 40 cm. The length of its hypotenuse is
(a) 16 cm
(b) 18 cm
(c) 17 cm
(d) Data insufficient

B

Question. Which of the following is/are not correct?
(a) If the diagonals of a quadrilateral divide each other proportionally, then it is a trapezium.
(b) The line segments joining the mid-points of the adjacent sides of a quadrilateral form a parallelogram.
(c) If corresponding sides of two similar triangles are in the ratio 4 : 5, then corresponding medians of the triangles must be in the ratio 4 : 5.
(d) None of the above

D

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

A

Question. In the given figure, AD is the bisector of ∠A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, determine AC

(a) 4.5 cm
(b) 3.5 cm
(c) 4.8 cm
(d) 3.2 cm

A

Fill in the Blanks :

Question. Line joining the mid-points of any two sides of a triangle is …………. to the third side.

parallel

Question. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the …………. ratio.

same

Question. All circles are ………………

similar

Question. In DABC, AB = 6 3 m, AC = 12 cm and BC = 6 cm, then ∠B = ……………… .

[90°]

Question. All squares are ………………

similar

True or False :

Question. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

True

Question. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O, OA /OC=OB/ OD = .

True

Question. All the congruent figures are similar but the converse is not true.

True

Question. If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.

True

Question. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.