Symmetry Class-7 ML Aggarwal ICSE Mathematics Solutions Chapter-14. We provide step by step Solutions of Exercise / lesson-14 Symmetry ICSE Class-7th  ML  Aggarwal Maths..

Our Solutions contain all type Questions with Exe-14.1 , Exe-14.2,  Objective Type Questions ( including Mental Maths and Multiple Choice Questions ) and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7 Mathematics.

## Symmetry Class-7 ML Aggarwal ICSE Mathematics Solutions Chapter-14

–: Select Topic :–

Exercise 14.1 ,

Exercise-14.2,

Objective Type Questions,

Mental Maths,

Multiple Choice Questions ,(MCQ)

### Ex 14.1, Symmetry Class-7 ML Aggarwal ICSE Mathematics Solutions

Question 1.
Draw all lines of symmetry, if any, in each of the following figures:

The line/lines of symmetry have been drawn as given below:

Question 2.
Copy the figures with a punched hole(s) and draw all the axes of symmetry in each of the following:

The line/lines of symmetry have been drawn as given below:

Question 3.
In the following figure, mark the missing hole(s) in order to make them symmetrical about the dotted line:

The lines of symmetry have been drawn and the required holes are
marked by dark punches (small circles) as given below:

Question 4.
In the following figures, the mirror line (line of symmetry) is given as dotted line. Complete each figure by performing reflection in the mirror (dotted) line and name the figure you complete:

Each figure is given, has been completed along with the mirror (dotted) line:

Question 5.
Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals?

We get the same figure if we shade according to the
other diagonal as a line of symmetry.
Also, we get the same figure of we shade
by taking the line joining the mid-point of the opposite sides.
Yes, the figure is symmetrical about both diagonals.

Question 6.
Draw the reflection of the following figures/letter in the given mirror line shown dotted:

The reflection of the given figure/letter in the given mirror line shown
dotted have been drawn as given below:

Question 7.
What other names can you give to the line of symmetry of
(i) an isosceles triangle
(ii) rhombus
(iii) circle?

(i) An isosceles triangle: We can be called the line of symmetry
as the angle bisector or median of the triangle.
(ii) Rhombus: The lines of symmetry of the rhombus are
also called as the diagonals of the rhombus as they bisect each other at right angles.
(iii) Circle: The lines of symmetry of a circle are also called the diameters of the circle.
As the diameter of a circle is infinite, so the lines of symmetry of a circle are also infinite.

### Symmetry Class-7 ML Aggarwal ICSE Mathematics Solutions Ex 14.2

Question 1.
Which of the following figures have rotational symmetry? In case of rotational symmetry, find the order of rotational symmetry.

(i) In figure (i) the rotational symmetry is of order is 2.
(ii) In figure (ii) the rotational symmetry is of order 2.
(iii) In figure (iii) there is no rotational symmetry.
(iv) In figure (iv) the rotational symmetry is of order 2.
(v) In figure (v) there is no rotational symmetry.
(vi) In figure (vi) there is rotational symmetry of order 4.
(vii) In figure (vii) there is rotational symmetry of order 1.
(viii)In figure (viii) there is no rotational symmetry.
(ix) In figure (ix) there is rotational symmetry of order 2.
(x) In figure (x) there is rotational symmetry of order 4.
(xi) In figure (xi) there is rotational symmetry of order 6.
(xii) In figure (xii) there is rotational symmetry of order 4.

#### Question 2.

Which of the following figures have rotational symmetry of order greater than 1?

Solution:
From the given figure,
Figure (i) and (iv) i.e., rhombus and circle have
rotational symmetry more than order 1.
A rhombus has 2 and a circle has many.

Question 3.
Name any two figures that have both lines of symmetry and rotational symmetry.

Rhombus and an equilateral triangle have
both line of symmetry and rotational symmetry.

Question 4.
Name the quadrilaterals which have both line and rotational symmetry of order more than 1.

In a quadrilateral, rectangle, square and rhombus have both line of symmetry
as well as rotational symmetry.

Question 5.
Draw a rough sketch of:
(i) a triangle with both line and rotational symmetries of order more than 1.
(ii) a triangle with only one line of symmetry and no rotational symmetry of order more than 1.
(iii) a triangle with no line symmetry but rotational symmetry of order 1.
(iv) a quadrilateral with no line symmetry but rotational symmetry of order more than 1.
(v) a quadrilateral with line symmetry but not rotational symmetry of order more than 1.

(i) A triangle with both line and
rotational symmetry of order more than 1.
It is an equilateral triangle.

(ii) A triangle with only one line of symmetry
but no rotational symmetry of order more than 1.
It is an isosceles triangle.

(iii) A triangle having no line symmetry
but rotational symmetry of order 1.
It is a scalene triangle.

(iv) A quadrilateral with no line symmetry
but rotational symmetry of order more than 1.
It is a parallelogram.

(v) A quadrilateral, with the line of symmetry
but not rotational symmetry of order more than 1.
It is an isosceles trapezium.

Question 6.
If a figure has two or more than two lines of symmetry, can it have rotational symmetry of order more than one?

If it has two or more lines of symmetry, then,
yes, it can have rotational symmetry of order more than one.
A circle is its example.

Question 7.
A figure looks exactly the same as its original figure after rotation of 60°. At what other angles will this figure appear the same?
What can you say if the angle of rotation is
(i) 72°
(ii) 45°
(iii) 50°?

A figure looks exactly the same as its original after rotation of 60°.
It will also like the same after rotation of 120°, 180°, 240°, 300°, and 360°.
(i) If the angle of rotation of symmetry is 72°
then it will look exactly the same after it rotates after 144°, 216°, 288°, 360°.
(ii) If the angle of rotation of symmetry is 45°,
then it will look exactly the same after 90°, 135°, 180°, 225°, 270°, 315°, and 360°.
(iii) If the angle of rotation is 50°, then it is not possible.

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