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**Ncert exemplar Solutions Class 6 Mathematics Symmetry and Practical Geometry**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of NCERT Class 6 Mathematics Book, Unit 9, Symmetry and Practical Geometry. Here students can easily find step by step solutions of all the problems for Symmetry and Practical Geometry, Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get Unit 9 solutions.

**Symmetry and Practical Geometry Unit 9 Solution :**

**Multiple Choice Questions : **

**Question no – (2) **

**The number of lines of symmetry in a scalene triangle is**

**Solution : **

Scalene triangle is the triangle having all sides are of different lengths.

Scalene triangle has No lines of symmetry.

The number of lines of symmetry in a scalene triangle is 0.

Hence, correct answer is option (A) 0

**Question no – (3)**

** The number of lines of symmetry in a circle is**

**Solution : **

In circle infinite number of lines of symmetry.

The number of lines of symmetry in a circle is more than 4

Thus, the correct answer is option (D) more than 4.

**Question no – (4)**

**Which of the following letters does not have the vertical line of symmetry**

**Solution : **

E has not vertical line of symmetry.

Hence, correct answer is option – (C) E

**Question no – (5) **

**Which of the following letters have both horizontal and vertical lines of symmetry**

**Solution : **

X has both horizontal and vertical lines of symmetry.

Thus, the correct answer is option (A) X

**Question no – (6) **

**Which of the following letters does not have any line of symmetry**

**Solution : **

Only letter S does not have any line of symmetry.

So, the correct answer is option – (B) S

**Question no – (7) **

**Which of the following letters has only one line of symmetry?**

**Solution : **

T Has only one line of symmetry.

Hence, correct answer is option (D) T

**Question no – (8) **

**The instrument to measure an angle is a**

**Solution : **

The instrument to measure an angle is a Protractor.

So, the correct answer is option – (B) Protractor.

**Question no – (9)**

** The instrument to draw a circle is**

**Solution : **

The instrument to draw a circle is Compasses.

So, the correct answer is option (D) Compasses

**Question no – (10) **

**Number of set squares in the geometry box is**

**Solution : **

Number of set squares in the geometry box is 2.

So, the correct answer is option – (C) 2

**Question no – (11) **

**The number of lines of symmetry in a ruler is**

**Solution : **

The number of lines of symmetry in a ruler is 2.

Ruler is a rectangular shape.

Hence, correct answer is option – (C) 2

**Question no – (12) **

**The number of lines of symmetry in a divider is**

**Solution : **

The number of lines of symmetry in a divider is 1.

Thus, the correct answer is option – (B) 1

**Question no – (13) **

**The number of lines of symmetry in compasses is**

**Solution : **

The number of lines of symmetry in compasses is 0.

So, the correct answer is option – (A) 0

**Question no – (14)**

** The number of lines of symmetry in a protractor is**

**Solution : **

The number of lines of symmetry in compasses is 0.

So, the correct answer is option – (A) 0

**Question no – (15) **

**The number of lines of symmetry in a protractor is**

**Solution : **

The number of lines of symmetry in a 45° – 45° – 90° set-square is 1.

So, the correct answer is option – (B) 1

**Question no – (16) **

**The number of lines of symmetry in a 30° – 60° – 90° set square is**

**Solution : **

The number of lines of symmetry in a 30° – 60° – 90° set square is 0.

Hence, correct answer is option – (A) 0

**Question no – (17) **

**The instrument in the geometry box having the shape of a triangle is called a**

**Solution : **

The instrument in the geometry box having the shape of a triangle is called a Set-square.

So, the correct answer is option – (D) Set-square

**Fill in the blanks :**

**Question no – (18) **

**Solution : **

The distance of the image of a point (or an object) from the line of symmetry (mirror) is **Equal** (same) as that of the point (object) from the line (mirror).

**Question no – (19) **

**Solution : **

The number of lines of symmetry in a picture of Taj Mahal is** 1.**

If we cut the Taj Mahal it get divided in exactly two identical shapes.

**Question no – (20) **

**Solution : **

The number of lines of symmetry in a rectangle and a rhombus are **Equal.**

Because, Rectangle has 2 lines of symmetry. Rhombus also 2 lines of symmetry.

**Question no – (21) **

**Solution : **

The number of lines of symmetry in a rectangle and a square are **unequal.**

Because, Rectangle has 2 lines of symmetry and Square has more than 2 lines of symmetry.

**Question no – (22) **

**Solution : **

We know, The distance of the image of a point (or an object) from the line of symmetry (mirror) is Equal (same) as that of the point (object) from the line (mirror).

If a line segment of length 5 cm is reflected in a line of symmetry (mirror), then its reflection (image) is a **line**__ __**segment** of length **5 cm.**

**Question no – (23) **

**Solution : **

We know, The distance of the image of a point (or an object) from the line of symmetry (mirror) is Equal (same) as that of the point (object) from the line (mirror).

If an angle of measure 80° is reflected in a line of symmetry, then the reflection is an **angle** of measure **80°.**

**Question no – (24) **

**Solution : **

The image of a point lying on a line l with respect to the line of symmetry l lies on Line **l.**

**Question no – (25) **

**Solution : **

In Fig. 9.10, if B is the image of the point A with respect to the line l and P is any point lying on l, then the lengths of line segments PA and PB are **Equal.**

We know, The distance of the image of a point (or an object) from the line of symmetry (mirror) is Equal (same) as that of the point (object) from the line (mirror).

Point p lies on a same distance from point A and Point B.

Lengths of line segments PA and PB are equal.

PA = PB

**Question no – (26) **

**Solution : **

The number of lines of symmetry in Fig. 9.11 is **5**

**Question no – (27) **

**Solution :**

The common properties in the two set-squares of a geometry box are that they have a **Right angle** and they are of the shape of a **Triangle.**

There are 2 types of set – squares in geometry box.

30° – 60° – 90° set square

45° – 45° – 90° set square

In this Right angle is common.

Shape of set squares is Triangle.

**Question no – (28) **

**Solution :**

The digits having only two lines of symmetry are **0** and** 8.**

Only 0 and 8 has two lines of symmetry.

**Question no – (29) **

**Solution :**

The digit having only one line of symmetry is **3.**

3 has only one line of symmetry.

**Question no – (30) **

**Solution :**

The number of digits having no line of symmetry is **1 ,2, 4, 5, 6, 7, 9**

**Question no – (31) **

**Solution :**

The number of capital letters of the English alphabets having only horizontal line of symmetry is** 5.**

B, C, D, E, K

This 5 Letters having only horizontal line of symmetry.

**Question no – (32) **

**Solution :**

The number of capital letters of the English alphabets having only vertical line of symmetry is **7.**

A, M, T, U, V, W, Y

This 7 Letters having only vertical line of symmetry.

**Question no – (33) **

**Solution :**

The number of capital letters of the English alphabets having both horizontal and vertical lines of symmetry is** 4.**

H, I, O, X

This Letters having both horizontal and vertical lines of symmetry.

**Question no – (34) **

**Solution :**

The number of capital letters of the English alphabets having no line of symmetry is **10.**

F, G, J, L, N, P, Q, R, S, Z – This 10 letters having no line of symmetry.

**Question no – (35) **

**Solution :**

The line of symmetry of a line segment is the **Perpendicular** bisector of the line segment.

**Question no – (36) **

**Solution :**

The number of lines of symmetry in a regular hexagon is **6.**

Because, Regular hexagon has 6 sides.

**Question no – (37) **

**Solution :**

The number of lines of symmetry in a regular polygon of n sides is** n.**

The number of lines of symmetry in a regular polygon is equal to sides present in regular polygon.

**Question no – (38) **

**Solution :**

A protractor has **1** line of symmetry

Because, Protractor is half circle.

**Question no – (39) **

**Solution :**

A 30° – 60° – 90° set-square has__ __**0**__ __line of symmetry.

**Question no – (40) **

**Solution : **

A 45° – 45°- 90° set-square has** 1**__ __line of symmetry.

**Question no – (41) **

**Solution : **

A rhombus is symmetrical about **Diagonals.**

**Question no – (42) **

**Solution : **

A rectangle is symmetrical about the lines joining the **Mid Points** of the opposite sides.

**State True or False :**

**Question no – (43) **

**Solution : **

A right triangle can have at most one line of symmetry

This statement is **True.**

**Question no – (44) **

**Solution : **

A kite has two lines of symmetry

This statement is **False.**

Because, A kite has One lines of symmetry.

**Question no – (45) **

**Solution : **

A parallelogram has no line of symmetry

This statement is **True.**

**Question no – (46) **

**Solution : **

If an isosceles triangle has more than one line of symmetry, then it need not be an equilateral triangle.

This statement is **False.**

Because, If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle.

**Question no – (47) **

**Solution : **

If a rectangle has more than two lines of symmetry, then it must be a square

This statement is **True.**

**Question no – (48) **

**Solution : **

With ruler and compasses, we can bisect any given line segment

This statement is **True.**

**Question no – (49) **

**Solution : **

Only one perpendicular bisector can be drawn to a given line segment

This statement is **True.**

**Question no – (50) **

**Solution : **

Two perpendiculars can be drawn to a given line from a point not lying on it

This statement is **False.**

Because, Only one perpendiculars can be drawn to a given line from a point not lying on it.

**Question no – (51) **

**Solution : **

Two perpendiculars can be drawn to a given line from a point not lying on it

This statement is **False.**

Only one perpendiculars can be drawn to a given line from a point not lying on it.

**Question no – (52) **

**Solution : **

Using only the two set-squares of the geometry box, an angle of 15° can be drawn

This statement is **True.**

**Question no – (53) **

**Solution : **

Using only the two set-squares of the geometry box, an angle of 40° can be drawn

This statement is **False.**

Because, Using only the Protractor of the geometry box, an angle of 40° can be drawn.

**Question no – (54) **

**Solution : **

If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle

This statement is **True.**

**Question no – (55) **

**Solution : **

A square and a rectangle have the same number of lines of symmetry

This statement is **False.**

Because, A square and a rectangle have the Different number of lines of symmetry.

**Question no – (56) **

**Solution : **

A circle has only 16 lines of symmetry

This statement is **False.**

Because, A circle has infinite number of lines of symmetry.

**Question no – (57) **

**Solution : **

A 45° – 45° – 90° set-square and a protractor have the same number of lines of symmetry

This statement is **True.**

**Question no – (58) **

**Solution : **

It is possible to draw two bisectors of a given angle

This statement is **False.**

Because, It is not possible to draw two bisectors of a given angle.

**Question no – (59) **

**Solution : **

A regular octagon has 10 lines of symmetry

This statement is **False.**

Because, A regular octagon has 8 lines of symmetry.

In regular polygon number of lines of symmetry is equal to number of sides of regular polygon.

Regular octagon has 8 sides hence, 8 lines of symmetry.

**Question no – (60) **

**Solution : **

Infinitely many perpendiculars can be drawn to a given ray.

This statement is **True.**

**Question no – (61) **

**Solution : **

Infinitely many perpendicular bisectors can be drawn to a given ray.

This statement is **False.**

Because, Only one perpendicular bisectors can be drawn to a given ray.

**Question no – (62) **

**Solution : **

Yes, Only One line of symmetry in above figure.

**Question no – (63) **

**Solution : **

In above rectangle PQRS,

There are 2 Lines of symmetry.

Line AC and Line BD are 2 lines of symmetry.

**Question no – (64) **

**Solution : **

The number of capital letters of the English alphabets having both horizontal and vertical lines of symmetry is 4.

H, I, O, X – These letters having more than one line of symmetry.

**Question no – (65) **

**Solution : **

MATHEMATICS

Here only letter ‘S‘ has no line of symmetry.

**Question no – (66) **

**Solution : **

SYMMETRY word consist of S, Y, M, E, T, R, Y

S – Has no line of symmetry.

Y – Has 1 line of symmetry.

M – Has 1 line of symmetry.

E – Has 1 line of symmetry.

T – Has 1 line of symmetry.

R – Has no line of symmetry.

**Question no – (67) **

**Solution : **

**(i)** → **(f)** 1

**(ii)** → **(c)** 4

**(iii)** → **(f)** 1

**(iv)** → **(d)** 3

**(v)** → **(e)** 2

**(vi)** → **(a)** 6

**Question no – (68) **

**Solution : **

**(i)** The Ruler – Has 2 lines of symmetry

**(ii)** The Divider – Has 1 lines of symmetry

**(iii)** The Compasses – Has 0 lines of symmetry

**(iv)** The protractor – Has 1 lines of symmetry

**(v)** Triangular piece with two equal sides – Has 1 lines of symmetry

**(vi)** Triangular piece with unequal sides – Has 0 lines of symmetry

**Question no – (69) **

**Solution : **

AB and A’B’ are equal

**Question no – (70) **

**Solution : **

**(a)** Is the image of P in line l the point P itself?

= Yes. The image of P in line l the point P itself.

**(b)** Is PA = PC?

= Yes.

PA = PC

= Because point p lie in the same distance from point A and Point C.

**(c)** Is PA + PB = PC + PB?

= Yes.

= PA + PB = PC + PB

= Because point p lie in the same distance from point A and Point C.

**(d)** Is P that point on line l from which the sum of the distances of points A and B is minimum?

= Yes.

**Previous Chapter Solution : **