# Symmetry Class-8 RS Aggarwal ICSE Maths Goyal Brothers

**Symmetry Class-8 RS Aggarwal** ICSE Maths Goyal Brothers Prakashan Solutions Chapter-20. We provide step by step Solutions of Exercise / lesson-20 **Symmetry** for ICSE **Class-8 RS** **Aggarwal** Maths.

Our Solutions contain all type Questions of Exe-20 with Notes to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

**Symmetry Class-8 RS Aggarwal** ICSE Maths Goyal Brothers Prakashan Solutions Chapter-20

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**Notes on Symmetry**

**Symmetry** is defined as a balanced and a proportionate similarity which is found in two halves of an object, that is, one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the **symmetrical** halves is called the line of **symmetry**

### Line of Symmetry

The imaginary line or axis along which you fold a figure to obtain the symmetrical halves is called the line of symmetry. It basically divides an object into two mirror-image halves. The line of symmetry can be vertical, horizontal or diagonal. There may be one or more lines of symmetry

### Types of Symmetry

Symmetry may be viewed when you flip, slide or turn an object. There are types of Symmetry which are:

- Reflexive
- Rotational Symmetry

**Reflective or Line**: A figure is symmetrical about a dotted line which divides it into two equal halves. This is often referred to as the basic type.

**Rotational Symmetry:** You rotate a shape about an axis and it appears exactly the same as it did before rotation. Example: a square, a rectangle, etc

Rotation, like the movement of the hands of a clock, is called a clockwise rotation; otherwise, it is said to be anticlockwise

A number of other kinds of symmetric types exist such as the point, translational, glide reflectional, helical, etc

**Lines of Symmetry for Regular Polygons**

Regular polygons have equal sides and equal angles. They have multiple (i.e., more than one) lines of symmetry. Each regular polygon has as many lines of symmetry as it has sides.

Regular Polygon |
Regular Hexagon |
Regular Pentagon |
Square | Equilateral Triangle |

Number of Lines of Symmetry | 6 | 5 | 4 | 3 |

Lines of Symmetry of some Irregular Polygons.

**Lines of Symmetry of some Alphabet**

Each of the following capital letters of the English alphabet is symmetrical about the dotted line or lines as shown:

**Lines of Symmetry of some regular Polygons.**

** **In a complete turn (of 360°), the number of times an object looks exactly the same is called the order of rotational symmetry.

**Exe-20, Symmetry Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions**

**Exe-20, Symmetry Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions**

**Question 1:**

Which or the following geometrical figures has exactly one line of symmetry ?

(i) A rectangle

(ii) A semicircle

(iii) A regular pentagon

(iv) A rhombus

**Answer :**

(ii) A semicircle has one line of symmetry As a rectangle has two lines of symmetry, pentagon has one and a rhombus has two.

**Question 2:**

Which of the following geometrical figure has exactly two lines of symmetry ?

(i) A square

(ii) A parallelogram

(iii) An isosceles trapezium

(iv) A rectangle.

**Answer : **

(iv) A rectangle has two lines of symmetry. As a square has four lines of symmetry, a parallelogram has no line of symmetry, and an isosceles trapezium has one line of symmetry.

**Question 3:**

An equilateral triangle has three lines of symmetry, an isosceles triangle will have:

(i) No line of symmetry

(ii) one line of symmetry

(iii) Two lines of symmetry

(iv) Three lines of symmetry

**Answer : **

(ii) An isosceles triangle has only one line of symmetry.

**Question 4:**

**A square and a rectangle have :**

(i) only one line of symmetry

(i) Two lines of symmetry each

ii) Four lines of symmetry each

(i) An unequal number of lines of symmetry.

**Answer : **

(iv) An unequal number of lines of symmetry. As, a square has four lines of symmetry while a rectangle has two lines of symmetry.

**Question 5:**

Which of the following letters of English alphabet does not passes a linear symmetry ?

(i) C

(ii) M

(iii) S

(iv) B

**Answer : **

**(iii) S **has no line of symmetry.

**Question 6:**

Draw all possible lines of symmetry in each of the following figure and state the number of lines of symmetry in each case :

**Answer : **

(i) In this figure one line symmetry

(ii) In this figure no line symmetry

(iii) In this figure one line symmetry

(iv) In this figure one line symmetry

**Question 7:**

Construct a triangle POR such that, QR = 4 cm, ∠Q = 45° and R 90° Draw the lines ot symmetry for this triangle.

**Answer : **

**Construction :**

(i) Draw a line segment QR = 4 cm

(ii) At Q, draw a ray making an angle of 45° and at R, a ray making an angle of 90° meeting each other at P.

△ POR is the required triangle.

(iii) From R, draw a perpendicular bisector of PQ.

This is the required line of symmetry.

**Question 8:**

Construct a triangle XYZ such that XY = 3.5 cm and ∠X = ∠Y = 65°. Draw the lines of symmetry for this triangle.

**Answer : **

**Construction :**

(i) Draw a line segment XY = 3.5 cm

(ii) At X and Y, draw rays making an angle of 65° each meeting each other at Z.

△ XYZ is the required triangle.

(iii) From 7, draw perpendicular bisector of XY.

This is required line of symmetry.

**Question 9:**

** C**onstruct an angle ∠ PQR = 80°. Draw its line of symmetry if PQ = QR = 6.5 cm.

**Answer : **

**Construction :**

(i) Draw a line segment PQ = 6.5 cm

(ii) At Q draw a ray making an angle of 80 and cut off QR = 6.5 cm and join PR.

(iii) Draw the angle bisector of ∠ PQR.

This is the required line of symmetry.

**Question 10:**

State and explain the type of symmetry possessed by each of the following figures.

**Answer : **

(i)

(a)** Linear symmetry:** It has no line of symmetry.

(b)** Point symmetry** : It has point O which is the centre of symmetry

(c) **Rotational symmetry :** It has rotational symmetry of order 3 above the point O.

(ii)

(a) **Linear symmetry** : It has two lines of symmetry

i.e. The line joining C and H and the line joining the mid points of AJ and EF.

(b) **Point symmetry**: It has point O which is the point of symmetry.

(c) **Rotational symmetry** : has rotational symmetry of order 2 about the point o

(iii)

(a) **Linear symmetry** : It has no line of symmetry.

(b) **Point symmetry:** Point O is the point of symmetry.

(c) **Rotational symmetry**: lt has rotational symmetry of order 2 about the point O.

(iv)

(a) **Linear symmetry:** Three lines of symmetry which are the lines joining AD, BE and CF.

(b) **Point symmetry** : It has no point symmetry.

(c)** Rotational symmetry:** It has a rotational symmetry of order three about the point O.

(v)

(a) **Linear symmetry:** It has no line of symmetry.

(b) **Point symmetry:** It has no point of symmetry

(c)** Rotational symmetry** : It has a rotational symmetry of order 3 about the point O.

(vi)

(a) **Linear symmetry:** It has no line of symmetry.

(b) **Point symmetry** : At O, the point symmetry

(c) **Rotational symmetry** : It has a rotational symmetry order 2 about the point O.

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