### FEATURED POST ON MATHS MCQ

### Maths MCQ Ch-6 Class 10 | Triangle

- Get link
- Other Apps

**Mathematics**

**Multiple Choice Questions (MCQ)**

**Class 10 | Chapter 6 | Triangles**

**MCQ Based on Basic Proportionality Theorem or Thales Theorem(BPT)**

**MCQ Based on the Similarity of Triangles**

**MCQ Based on the Ratio of Areas of two similar Triangles**

**MCQ Based on the Pythagoras Theorem and its Converse.**

**MCQ Based from the CBSE Sample Questions**

**In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. Solution Hints are also given to some difficult problems. Each MCQ contains four options from which one option is correct. On the right hand side column of the pdf Answer option is given.**

**Action Plan**

**First of all students should Learn and write all basic points and Formulas related to the Triangles**

**Start solving the NCERT Problems with examples.**

**Solve the important assignments on the Similarity of Triangles.**

**Then start solving the following MCQ.**

# 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

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.

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

a) False

b) True

Q 5) If ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R then, ∆ABC & ∆PQR are similar according to which test?

a) AAA test

b) AA test

c) SAS test

d) SSS test

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.

a) 2.3 cm

b) 5.1 cm

c) 11.74 cm

d) 10.9 cm

(a) 2.5

(b) 3

(c) 5

(d) 6

a) 34 m

b) 28 m

c) 30 m

d) 26 m

Q 11) The diagonals of a rhombus are 16 cm and 12 cm, in length. The side of rhombus in length is:

(a) 20 cm

(b) 8 cm

(c) 10 cm

(d) 9 cm

Ans: c

Solution Hint

Since diagonals of a rhombus bisects each other at right angle

By Pythagoras theorem,

(16/2)

^{2}+ (12/2)

^{2}= side

^{2}

^{2}+ 6

^{2}= side

^{2}

^{2}

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.

a) AAA test

b) AA test

c) SAS test

d) SSS test

a) a = c / b

b) ab = cx

c) bx = ac

d) cb = ax

(a) 230 sq.cm.

(b) 106 sq.cm

(c) 107 sq.cm.

(d) 108 sq.cm

a) 11.23 cm

b) 15.24 cm

c) 14.375 cm

d) 14.275 cm

a) 12 cm

b) 16 cm

c) 18 cm

d) 20 cm

(a) √3/2 a

(b) √3/2 a

^{2}

(c) √3/4 a

^{2}

(d) √3/4 a

a) 19 : 23

b) 23 : 19

c) 361 : 529

d) 15 : 23

(a) 30 cm

(b) 40 cm

(c) 50 cm

(d) 60 cm

b) 1 : 3

c) 1 : 2

d) 2 : 1

a) 4.8 cm

b) 5.6 cm

c) 3.8 cm

d) 5.4 cm

(a) 120°

(b) 60°

(c) 90°

(d) 45°

(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

a) 6 : 7

b) 7 : 6

c) 36 : 49

d) 49 : 36

(a) 4.33 cm

(b) 3.9 cm

(c) 5 cm

(d) 4 cm

a) 8 cm

b) 8.5 cm

c) 7 cm

d) 7.5 cm

a) 4 : 1

b) 1 : 2

c) 2 : 1

d) 1 : 4

(a) ∠A = ∠F

(b) ∠B = ∠D

(c) ∠A = ∠D

(d) ∠B =∠E

a) 2.34 cm

b) 3.45 cm

c) 5√2 cm

d) 2.45 cm

Ans: c

Solution Hint

Radius = 5 cm, Diameter = 10 cm ⇒ AC = 10 cm

Let side of square = x ⇒ AB = BC = x

By Pythagoras theorem

AB

^{2}+ BC

^{2}= AC

^{2}

^{2}+ x

^{2}= 10

^{2}

^{2}= 100 ⇒ x

^{2}= 50 ⇒ x = 5√2

^{2}and 81cm

^{2}respectively and the length of QR is 15cm.

b) 40/6

c) 4/3

d) 40/3

(a) 2 : 3

(b) 4 : 9

(c) 81 : 16

(d) 16 : 81

^{2}and 64cm

^{2}. If the altitude of the larger triangle is 5.5 cm, then what will be the altitude of the corresponding smaller triangle?

c) 2.4 cm

Ans: a

Solution Hint ratio of areas of similar triangles is equal to the ratio of the squares of their corresponding altitudes.

(a) Circles

(b) Squares

(c) Equilateral triangles

(d) Isosceles triangles

^{2}and 121cmx

^{2}. If the median of the bigger triangle is 10 cm, then what will be the corresponding median of the smaller triangle?

b) 10 / 11

c) 50 / 11

d) 5 / 11

Ans: c

Solution Hint ratio of areas of similar triangles is equal to the ratio of the squares of their corresponding medians.

(a) BD . CD = BC

^{2}

(b) AB . AC = BC

^{2}

(c) BD . CD = AD

^{2}

(d) AB . AC = AD

^{2}

Q 37) ∆ABC ∼ ∆PQR, AD & PS are the angle bisectors of respectively. If AD = 1.5cm and PS = 2.3 cm then, what will be the ratio of the areas of ∆ABC and ∆PQR?

a) 19 : 15

b) 225 : 529

c) 529 : 225

d) 15 : 17

Ans: b

Solution Hint Areas of similar triangles is equal to the ratio of the squares of their corresponding angle bisectors.

(a) congruent but not similar

(b) similar but not congruent

(c) neither congruent nor similar

(d) congruent as well as similar

a) 16 : 9

b) 7 : 3

c) 49 : 9

d) 9 : 49

(a) 16

(b) 4

(c) 1/ 4

(d) 1/ 16

Ans: a

Solution Hint

Given, ΔABC ~ ΔPQR

and BC / QR = 1/4

Ratio of area of similar triangles is equal to the square of its corresponding sides. So, ar(ΔPRQ)/ar(ABC) = (QR/BC)

^{2}= (4/1)

^{2}= 16

a) cm

b) cm

c) cm

d) cm

Ans: a(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

a) 9 : 7

b) 7 : 9

c) 16 : 7

d) 16 : 9

(a)
AAA

(b)
SAS

(c)
SSS

(d)
ASA

(a)
square of the ratio of their corresponding sides

(b)
cube of the ratio of their corresponding sides

(c) square
root of the ratio of their corresponding sides

(d)
twice the ratio of their corresponding sides

a) 16 m

b) 8 m

c) 12 m

d) 15 m

a) 15 m

b) 5 m

c) 23 m

d) 13 m

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

a) 12 cm

b) 16 cm

c) 12.5 cm

d) 9.6 cm

Ans: d

Solution Hint

First Prove that ΔABC ~ ΔADB, then corresponding sides are proportional

a)
96 cm

b)
72 cm

c)
78 cm

d)
84 cm

a) 36 cm

b) 28.5 cm

c) 32.5 cm

d) 30 cm

Ans: c

Solution Hint:

a) 8.4 cm

b) 4 cm

c) 11 cm

d) 10 cm

Ans: d

Solution Hint

ABCD is a rhombus. The side of the rhombus is
13 cm and the length of one of its diagonal is 24 cm.

Let the length of other diagonal be 2x cm.

Since, diagonals of a rhombus bisect each other
at right angle.

Now, in ∆AED, by Pythagoras theorem

AD

^{2}= AE

^{2}+ DE

^{2}

13

^{2}= x

^{2}+ 12

^{2}(Since, AD is the altitude of the triangle it will bisect BC)

x

^{2}= 169 – 144 ⇒ x

^{2}= 25

x = √25 = 5 cm = AE

AC = 2 × AE = 2 × 5 = 10 cm

a) 8 m

b) 12 m

c) 7 m

d) 6 m

a) 6.40 cm

b) 5.25 cm

c) 2.44 cm

d) 3.29 cm

Ans: a

Solution Hint

Since, diagonals of a rhombus bisect each other at right angles.

Now, in ∆AED, by Pythagoras Theorem

AD

^{2}= AE

^{2}+ DE

^{2}

AD

^{2}= 4

^{2}+ 5

^{2}(Since, AD is the altitude of the triangle it will bisect BC)

AD

^{2}= 16 + 25 ⇒ AD

^{2}= 41

a) 13 m

b) 18 m

c) 15 m

d) 10 m

Ans: b

Questions From CBSE Sample Paper 2021-22

Basic Maths SP(241)

Ans: c

(a)
2 : 3

(b)
6 : 9

(c)
4 : 6

(d)
4 : 9

(a)
30m

(b)
50m

(c)
80m

(d)
100m

^{2 }= 2AC

^{2}, then the measure of angle C will be

(a)
30 ̊

(b)
45 ̊

(c)
60 ̊

(d)
90 ̊

(a)
7m

(b)
10m

(c)
17m

(d)
23m

(a)
2√3 cm

(b)
3√3 cm

(c)
4√3 cm

(d)
5√3 cm

(a)
2√2 cm

(b)
3√2 cm

(c)
2√3 cm

(d)
3√3 cm

(a)350m

(b)
250m

(c)
300m

(d)
225

altitude
of the rhombus is

(a)
12cm

(b)
12.8cm

(c)
19 cm

(d)
19.2cm

^{2}: PQ

^{2}= 4 : 9, then AM : PN =

(a)
16:81

(b)
4:9

(c)
3:2

(d)
2:3

(a)
7.5 cm

(b)
15 cm

(c)
22.5 cm

(d)
30 cm

(a) 7cm

(b)
6cm

(c)
4cm

(d)
3cm

(a) 22/3 cm

(b)
26/3 cm

(c)
55/3 cm

(d)
64/3 cm

(a) 32/3cm

(b)
16/3cm

(c)8/3cm

(d)
4/3cm

**THANKS FOR YOUR VISIT**

**PLEASE COMMENT BELOW**

**🙏**

- Get link
- Other Apps

## Comments

## Post a Comment