R d sharma solutions mathematics class 7 Solutions for Chapter 18 symmetry

Exercises in Chapter 18 symmetry Grade 7

Symmetry Exercise 18.1

Symmetry Exercise 18.2

Symmetry Exercise 18.3

Questions in Symmetry Exercise 18.1

State the number of lines of symmetry for the following figures:

(i) An equilateral triangle

(ii) An isosceles triangle

(iii) A scalene triangle

(iv) A rectangle

(v) A rhombus

(vi) A square

(vii) A parallelogram

(viii) A quadrilateral

(ix) A regular pentagon

(x) A regular hexagon

(xi) A circle

(xii) A semi-circle

What other name can you give to the line of symmetry of

(i) An isosceles triangle?

(ii) A circle?

Identify three examples of shapes with no line of symmetry.

Identify multiple lines of symmetry, if any, in each of the following figures:

Questions in Symmetry Exercise 18.2

In the following figures, the mirror line (i.e. the line of symmetry) is given as dotted line. Complete each figure performing reflection in the dotted (mirror) line. Also, try to recall name of the complete figure.

Each of the following figures shows paper cuttings with punched holes. Copy these figures on a plane sheet and mark the axis of symmetry so that if the paper is folded along it, then the wholes on one side of it coincide with the holes on the other side.

In the following figures if the dotted lines represent the lines of symmetry, find the other hole(s).

Questions in Symmetry Exercise 18.3

Give the order of rotational symmetry for each of the following figures when rotated about the marked point (x):

Name any two figures that have both line symmetry and rotational symmetry.

Give an example of a figure that has a line of symmetry but does not have rotational symmetry.

Give an example of a geometrical figure which has neither a line of symmetry nor a rotational symmetry.

Give an example of a letter of the English alphabet which has

(i) No line of symmetry

(ii) Rotational symmetry of order 2.

What is the line of symmetry of a semi-circle? Does it have rotational symmetry?

Draw, whenever possible, a rough sketch of

(i) a triangle with both line and rotational symmetries.

(ii) a triangle with only line symmetry and no rotational symmetry.

(iii) a quadrilateral with rotational symmetry but not a line of symmetry.

(iv) a quadrilateral with line symmetry but not rotational symmetry.

Fill in the blanks:

Figures	Centre of rotation	Order of rotation	Angle of rotation
Square	–	–	–
Rectangle	–	–	–
Rhombus	–	–	–
Equilateral Triangle	–	–	–
Regular hexagon	–	–	–
Circle	–	–	–
Semi-circle	–	–	–

Fill in the blanks:

English Alphabet Letter	Line Symmetry	Number of Lines of Symmetry	Rotational symmetry	Order of rotational symmetry
Z	Nil	0	Yes	2
S	–	–	–	–
H	Yes	–	Yes	–
O	Yes	–	Yes	–
E	Yes	–	–	–
N	–	–	Yes	–
C	–	–	–	–

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Chapters in this book

Integers

Fractions

Decimals

Rational Numbers

Operations on Rational Numbers

Exponents

Algebraic Expressions

Linear Equations In One Variable

Ratio and Proportion

Unitary Method

Percentage

Profit and Loss

Simple Interest

Lines and Angles

Properties of Triangle

Congruence

Constructions

Symmetry

Visualising Solid Shapes

Mensuration 1

Mensuration 2 Area of Circle

Data Handling-Collection Organisation Data

Data Handling-Central Values

Data Handling-Construction Of Bar Graphs

Data Handling-Probability

English Alphabet Letter	Line Symmetry	Number of Lines of Symmetry	Rotational symmetry	Order of rotational symmetry
Z	Nil	0	Yes	2
S	–	–	–	–
H	Yes	–	Yes	–
O	Yes	–	Yes	–
E	Yes	–	–	–
N	–	–	Yes	–
C	–	–	–	–

English Alphabet Letter	Line Symmetry	Number of Lines of Symmetry	Rotational symmetry	Order of rotational symmetry
Z	Nil	0	Yes	2
S	–	–	–	–
H	Yes	–	Yes	–
O	Yes	–	Yes	–
E	Yes	–	–	–
N	–	–	Yes	–
C	–	–	–	–

English Alphabet Letter	Line Symmetry	Number of Lines of Symmetry	Rotational symmetry	Order of rotational symmetry
Z	Nil	0	Yes	2
S	–	–	–	–
H	Yes	–	Yes	–
O	Yes	–	Yes	–
E	Yes	–	–	–
N	–	–	Yes	–
C	–	–	–	–