RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry

Exercise 17.1

 

Question 1:  List any four symmetrical objects from your phone or school. Also, mention the line of symmetry. 

Solution 1:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry


Question 2:  Identify the symmetrical instruments from your mathematical instrument box. 

Solution 2:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-


Question 3:  Copy each of the following on a squared paper and compute them in such a way that the dotted line is the line of symmetry.

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A

Solution 3:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A1

 

Exercise 17.2

 

Question 1:   Find the number of lines of symmetry in each of the following shapes.

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A2

Solution 1:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A5


Question 2:  Copy the following drawings on squared paper and complete each one of them in such a way that resulting figure has two dotted lines as two lines of symmetry: 

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A6

Solution 2:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A7

 

Exercise 17.3

 

Question 1:  Complete the following table:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A12

Solution 1:


RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A9

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A10

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A11


Question 2:   Consider the English alphabets A to Z. List among them the letters which have

(i) vertical line of symmetry. (like A)

(ii) horizontal lines of symmetry. (like B)

(iii) vertical and horizontal lines of symmetry. (like I)

(iv) no line of symmetry. (like Q) 

Solution 2:

(i) Vertical line of symmetry. (like A)

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A13

 

(ii) Horizontal lines of symmetry. (like B)

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A14

(iii) Vertical and horizontal lines of symmetry. (like I)

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A15

(iv) No line of symmetry. (like Q)

 RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A16

 

Question 3:  Can you draw a triangle having:

(i) exactly one line of symmetry

(ii) exactly two lines of symmetry.

(iii) three lines of symmetry.

(iv) no line of symmetry. 

Solution 3:

(i) An isosceles triangle has exactly one line of symmetry.

 RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A17

(ii) No there is no triangle having exactly two lines of symmetry. 

(iii) An equilateral triangle three lines of symmetry.

  RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A18

(iv) A scalene triangle has line of symmetry.

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A19


Question 4:  On a squared paper, sketch the following:

(i) A triangle with a horizontal line of symmetry but no vertical line of symmetry.

(ii) A quadrilateral with both horizontal and vertical lines of symmetry.

(iii) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

(iv) A hexagon with exactly two lines of symmetry.

(v) A hexagon with six lines of symmetry. 

Solution 4:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A20


Question 5:   Draw neat diagrams solving the line (or lines) of symmetry and give the specific name to the quadrilateral having:

(i) only one line of symmetry. How many such quadrilaterals are there?

(ii) its diagonals as the only lines of symmetry.

(iii) two lines of symmetry other than diagonals.

(iv) more than two lines of symmetry. 

Solution 5:

(i) Only one line of symmetry.

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A21

(ii) Diagonals as the only lines of symmetry:- Rhombus

 

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A22

(iii) Two lines of symmetry other than diagonals:- Rectangle

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A23

(iv) More than two lines of symmetry:- Square

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A24

 

Question 6:  Write the specific names of all the three quadrilaterals which have only one line of symmetry. 

Solution 6:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A25


Question 7:   Trace each of the following figures and draw the lines of symmetry, if any:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A26

Solution 7:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A27

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A28


Question 8:   On squared paper copy the triangle in each of the following figures. In each case draw the line(s) of symmetry if any and identify the type of the triangle.

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A30


Solution 8:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A29


Question 9:   Find the lines of symmetry for each of the following shapes:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A31

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A32

Solution 9:

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A33

RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry-A34


 

Question 10:   State whether the following statements are true or false:
(i) A right-angled triangle can have at most one line of symmetry.
(ii) An isosceles triangle with more than one line of symmetry must be an equilateral triangle.
(iii) A pentagon with one line of symmetry can be drawn.
(iv) A pentagon with more than one line of symmetry must be regular.
(v) A hexagon with line of symmetry can be drawn.
(vi) A hexagon with more than two lines of symmetry must be regular.
 
Solution 10:

(i) A right-angled triangle can have at most one line of symmetry. True
(ii) An isosceles triangle with more than one line of symmetry must be an equilateral triangle. True
(iii) A pentagon with one line of symmetry can be drawn. True
(iv) A pentagon with more than one line of symmetry must be regular. True
(v) A hexagon with line of symmetry can be drawn. True
(vi) A hexagon with more than two lines of symmetry must be regular. True


Objective Type Questions ::->
 

Mark the correct alternative in each of the following:

 

Question 1:  The total number of lines of symmetry of a scalene triangle is

(a) 1

(b) 2

(c) 3

(d) None of these 

Solution 1: (d) 

Number of Symmetry lines in a scalene triangle is 0.

 

Question 2:  The total number of lines of symmetry of an isosceles triangle is

(a) 1

(b) 2

(c) 3

(d) None of these

 

Solution 2: (a) 

Number of Symmetry lines in an isosceles triangle is 1.

 

Question 3:  An equilateral triangle is symmetrical about each of its

(a) altitudes

(b) medians

(c) angle bisectors

(d) all the above
 

Solution 3: (d) 

An equilateral triangle is symmetrical from altitudes, medians and angle bisectors. 

 

Question 4: The total number of lines of symmetry of a square is

(a) 1

(b) 2

(c) 3

(d) 4

 

Solution 4: (d) 

Number of Symmetry lines in a square is 4.

 

Question 5:  A rhombus is symmetrical about

(a) each of its diagonals

(b) the line joining the mid-points of its opposite sides

(c) perpendicular bisectors of each of its sides

(d) none of these

 

Solution 5: (a) 

A rhombus is symmetrical from its diagonals.

 

Question 6:  The number of lines of symmetry of a rectangle is

(a) 0

(b) 2

(c) 4

(d) 1

 

Solution 6: (b) 

Number of Symmetrical lines in a rectangle is 2.

 

Question 7:  The number of lines of symmetry of a kite is

(a) 0

(b) 1

(c) 2

(d) 3

 

Solution 7: (b) 

Number of Symmetrical lines in a kite is 1.

 

Question 8:  The number of lines of symmetry of a circle is

(a) 0

(b) 1

(c) 4

(d) unlimited

 

Solution 8: (d) 

Unlimited symmetrical lines can be form in a circle. 

 

Question 9:  The number of lines of symmetry of a regular hexagon is

(a) 1

(b) 3

(c) 6

(d) 8

 

Solution 9: (c) 

Hexagon has 6 symmetrical lines.

 

Question 10:  The number of lines of symmetry of an n-sided regular polygon is

(a) n

(b) 2n

(c) n/2

(d) none of these

 

Solution 10: (a) 

n side polygon has n symmetrical lines.

 

Question 11:  The number of lines of symmetry of the letter O of the English alphabet is

(a) 0

(b) 1

(c) 2

(d) 3

 

Solution 11: (c) 

2 symmetrical lines can be form in letter O.

 

Question 12:  The number of lines of symmetry of the letter Z of the English alphabet is

(a) 0

(b) 1

(c) 2

(d) 3

 

Solution 12: (a) 

We can’t make any symmetrical line in English alphabet letter Z.

RD Sharma Solutions Class 6 Maths
RD Sharma Solutions Class 6 Maths Chapter 1 Knowing our Numbers
RD Sharma Solutions Class 6 Maths Chapter 2 Playing with Numbers
RD Sharma Solutions Class 6 Maths Chapter 3 Whole Numbers
RD Sharma Solutions Class 6 Maths Chapter 4 Operations on Whole Numbers
RD Sharma Solutions Class 6 Maths Chapter 5 Negative Numbers and Integers
RD Sharma Solutions Class 6 Maths Chapter 6 Fractions
RD Sharma Solutions Class 6 Maths Chapter 7 Decimals
RD Sharma Solutions Class 6 Maths Chapter 8 Introduction to Algebra
RD Sharma Solutions Class 6 Maths Chapter 9 Ratio Proportion and Unitary Method
RD Sharma Solutions Class 6 Maths Chapter 10 Basic Geomatrical Concepts
RD Sharma Solutions Class 6 Maths Chapter 11 Angles
RD Sharma Solutions Class 6 Maths Chapter 12 Triangle
RD Sharma Solutions Class 6 Maths Chapter 13 Quadrilaterals
RD Sharma Solutions Class 6 Maths Chapter 14 Circles
RD Sharma Solutions Class 6 Maths Chapter 15 Pair of Lines and Transversal
RD Sharma Solutions Class 6 Maths Chapter 16 Understanding Three Dimensional Shapes
RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry
RD Sharma Solutions Class 6 Maths Chapter 18 Basic Geometrical Tools
RD Sharma Solutions Class 6 Maths Chapter 19 Geometrical Constructions
RD Sharma Solutions Class 6 Maths Chapter 20 Mensuration
RD Sharma Solutions Class 6 Maths Chapter 21 Data Handling Presentation of Data
RD Sharma Solutions Class 6 Maths Chapter 22 Data Handling Pictographs
RD Sharma Solutions Class 6 Maths Chapter 23 Data Handling Bar Graphs