Maths MCQ Ch-6 Class 10 | Triangle

Mathematics
MCQ | Class 10 | Ch-6 | Triangles

MCQ | CHAPTER 6 | TRIANGLES

Q 1) Which of the following triangles have the same side lengths?

(a) Scalene
(b) Isosceles
(c) Equilateral
(d) None of these

Ans: c

Q 2) Two congruent figures are similar when two similar figures are congruent.
a) True
b) False

Ans: a
Explanation: Two geometric figures are said to be similar if they are of same shape but different sizes and congruent if they have same shape and size.

Q 3) The figure shown is congruent.

     

a) True
b) False

Ans: a

Explanation The stars in the given figure are congruent because they are same shape and same size. Congruent figures have same shape and size

Q 6) The figure shown below is similar.

  

a) True
b) False

Ans: a
Explanation The two figures shown are similar because they have same shape but are different in sizes. The second pentagon is smaller in size as compared to a pentagon, but the basic structure of both the figures is same i.e. both are pentagon.

Q 7) In the given figure DE || BC, if AD = 5.9cm, DB = 4cm and AE = 7cm then, what will be the value of AC?

a) 2.3 cm                          

b) 5.1 cm           

c) 11.74 cm                      

d) 10.9 cm

Ans: c

Q 8) D and E are the midpoints of side AB and AC of a triangle ABC, respectively and BC = 6 cm. If DE || BC, then the length (in cm) of DE is:
(a) 2.5
(b) 3
(c) 5
(d) 6

Ans: b

Q 9) A man goes 10 m west and 24 m north. Find his distance from the starting point.
a) 34 m
b) 28 m
c) 30 m
d) 26 m

Ans: d

Q 10) What is the value of x id DE || BC ?

a) 0                     

b) 1                     

c) 2                     

d) 3

Ans: b

Q 11) The perimeters of two similar triangles ABC, PQR is 64 cm and 24 cm respectively. If PQ is 12 cm what will be the length of AB?
a) 30 cm
b) 32 cm
c) 12 cm
d) 16 cm

Ans: b

Solution Hint perimeters of similar triangles is the same as the ratio of their corresponding sides.

Q 12) ∆ABC is such that AB = 3 cm, BC = 2cm, CA = 2.5 cm. If ∆ABC ~ ∆DEF and EF = 4cm, then perimeter of ∆DEF is
(a) 7.5 cm

(b) 15 cm

(c) 22.5 cm

(d) 30 cm

 Ans: b

Q 13) If ∠D = ∠L, ∠E = ∠M then, ∆DEF & ∆LMN are similar according to which test?

a) AAA test
b) AA test
c) SAS test
d) SSS test

Ans: b

Q 14) In the given figure, LM || PQ, what will be the relation between x, a, b and c?

a) a = c / b
b) ab = cx
c) bx = ac
d) cb = ax

Ans: c

Q 15) In the figure, if DE|| BC, AD = 3cm, BD = 4cm and BC = 14 cm, then DE equals

(a) 7cm

(b) 6cm

(c) 4cm

(d) 3cm

Ans: b

Q 16) If DE || BC, AD = 4cm, BD = 7.5cm, AE = 6.4 cm & DE = 5cm then what will be the lengths of BC?

 a) 11.23 cm
b) 15.24 cm
c) 14.375 cm
d) 14.275 cm

Ans: c

Q 17) In ∆ ABC, DE || BC, AD = 4 cm, BD = 5 CM, DE = 8 CM Then BC =
a) 12 cm
b) 16 cm
c) 18 cm
d) 20 cm

Ans: c

Q 18) Area of an equilateral triangle with side length a is equal to:
(a) √3/2 a
(b) √3/2 a²
(c) √3/4 a²
(d) √3/4 a

Ans: c

Q 19) The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the altitude of the rhombus is

(a) 12cm
(b) 12.8cm
(c) 19 cm
(d) 19.2cm

Ans: d

Q 20) If perimeter of a triangle is 100 cm and the length of two sides are 30 cm and 40 cm, the length of third side will be:
(a) 30 cm
(b) 40 cm
(c) 50 cm
(d) 60 cm

Ans: a

Q 21) In two similar triangles ∆ABC and ∆DEF, AB = 15cm, DE = 5cm. If AL and DM are the altitudes of the triangles ABC, DEF respectively, then what will be the ratio of their altitudes?

a) 3 : 1
b) 1 : 3
c) 1 : 2
d) 2 : 1

Ans: a

Q 22) The perimeter of two similar triangles are 50 cm and 30 cm respectively. If one side of first triangle is 9 cm, then find the corresponding side of the other triangle.
a) 4.8 cm
b) 5.6 cm
c) 3.8 cm
d) 5.4 cm

Ans: d

Q 23) A vertical stick 20m long casts a shadow 10m long on the ground. At the same time a tower casts a shadow 50m long. What is the height of the tower?
(a) 30m
(b) 50m
(c) 80m
(d) 100m

Ans: d

Q 24) If triangles ABC and DEF are similar and AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, then find the perimeter of triangle ABC
(a) 22 cm
(b) 20 cm
(c) 21 cm
(d) 18 cm

Ans: d
Solution Hint: ABC ~ DEF
AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm
AB/DE = BC/EF = AC/DF
4/6 = BC/9 = AC/12
⇒ BC = (4 x 9)/6 = 6 cm
⇒ AC = (12 x 4)/6 = 8 cm
Perimeter = AB + BC + AC = 4 + 6 + 8 = 18 cm

Q 25) If ABC and DEF are two triangles and AB / DE = BC / FD, then the two triangles are similar if
(a) ∠A = ∠F
(b) ∠B = ∠D
(c) ∠A = ∠D
(d) ∠B =∠E

Ans: b

Q 26) Which of the following are not similar figures?
(a) Circles
(b) Squares
(c) Equilateral triangles
(d) Isosceles triangles

Ans: d

Q 27) In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 DE. 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

Ans: b

Q 28) It is given that ΔABC ~ ΔDFE, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true:
(a) DE = 12 cm, ∠F = 50°
(b) DE = 12 cm, ∠F = 100°
(c) EF = 12 cm, ∠D = 100°
(d) EF = 12 cm, ∠D = 30°

Ans: b

Solution Hint
Given, ΔABC ~ ΔDFE, ∠A =30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF= 7.5 cm
In triangle ABC,
∠A + ∠B + ∠C = 180°
∠B = 180° – 30° – 50° = 100°
Since ΔABC ~ ΔDFE, the corresponding angles are equal.
Thus, ∠D = ∠A = 30°
∠F = ∠B = 100°
∠E = ∠C = 50°
And
AB / DF = AC / DE
5 / 7.5 = 8 / DE DE = (8 × 7.5) / 5 = 12 cm

Q 29) Which of the following is not a similarity criterion for two triangles?

(a) AAA

(b) SAS

(c) SSS

(d) ASA 

Ans: d

Q 30) What will be the distance of the foot of ladder from the building, if the ladder is 10 m long reaches the top of a building 6 m high from the ground?
a) 16 m
b) 8 m
c) 12 m
d) 15 m

Ans: b

Q 31) The heights of two vertical lamp posts are 11 m and 6 m high. If the distance between them is 12 m, then what will be the distance between their tops?
a) 15 m
b) 5 m
c) 23 m
d) 13 m

Ans: d

Q 32) Which of triangle whose sides are given below are right angled?

a) AB = 3, AC = 8, BC = 6
b) AB = 5, AC = 12, BC = 15
c) AC = 7, AB = 24, BC = 25
d) AC = 7, AB = 24, BC = 26

Ans: c

Q 33) Sides of two similar triangles are in the ratio 4 : 5. If median of first triangle is 26 cm then find the corresponding median of the second triangle.
a) 36 cm
b) 28.5 cm
c) 32.5 cm
d) 30 cm

Ans: c

Solution Hint: When two triangles are similar then corresponding sides, medians, altitudes, angle bisectors and perimeters are proportional.

Q 34) A ladder 17m long reaches the top of the building 15m high from the ground. Find the distance of the foot of the ladder from the building.
a) 8 m
b) 12 m
c) 7 m
d) 6 m

Ans: a

Q 35) A man travels A to B, B to C, C to D and then finally D to E. What will be the shortest route the man could have taken?

a) 13 m
b) 18 m
c) 15 m
d) 10 m

Ans: b

Q 36) In the given figure, DE II BC. Which of the following is true?

 

Ans: c

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