NCERT Solutions For Class 6 Maths Chapter 13 Symmetry

Here at MentorAtHome, We provide NCERT Solutions For Class 6 Maths Chapter 13 Symmetry. NCERT solutions help students to improve their performance, and attain better results. In NCERT Solutions Class 6 Maths Chapter 13 there is 3 exercise.

NCERT Solutions For Class 6 Maths Chapter 13 Symmetry, we will discuss Symmetry. Symmetry is quite a common term used in day-to-day life. When we see certain figures with evenly balanced proportions, we say, They are symmetrical. Ch 13 Class 6 Maths solutions are important for understanding like the mirror image, Mirror reflection, and shapes.

NCERT Solutions For Class 6 Maths Chapter 13 Symmetry Exercises 13.1

Class 6th Maths Chapter 13 Solutions ex 13.1

Q.1. List any four symmetrical objects from your home or school.
Ans:-
The four symmetrical objects are
(a) Notebook
(b) Dining table
(c) A blackboard
(d) Wall clock
(e) A pair of scissors

Q.2. For the given figure, which one is the mirror line, l1 or l2?

Ans:-
In the following figure, l2 is the mirror line.

Q.3. Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well.


Ans:-
(a) Yes. It is symmetric
(b) Yes. It is symmetric
(c) No, it is not symmetric
(d) Yes. It is symmetric
(e) Yes. It is symmetric
(f) Yes. It is symmetric

Q.4. Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook in earlier classes. Then complete them such that the dotted line is the line of symmetry.

Ans:-

Q.5. In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.

Ans:-
The completed figure is as follows:

Q.6. In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric.

Ans:-
The required triangle may be drawn as follows to make it symmetric

NCERT Solutions For Class 6 Maths Chapter 13 Symmetry Exercises 13.2

NCERT Class 6 Maths Chapter 13 Solutions ex 13.2

Q.1. Find the number of lines of symmetry for each of the following shapes

Ans:-
(a) there are 4 lines of symmetry.
(b) there are 4 lines of symmetry.
(c) there are 4 lines of symmetry.
(d) there is only 1 line of symmetry.
(e) there are 6 lines of symmetry.
(f) there are 6 lines of symmetry.
(g) there is no line of symmetry.
(h) there is no line of symmetry.
(i) there are 3 lines of symmetry.

Q.2. Copy the triangle in each of the following figures on squared paper. In each case, draw the line(s) of symmetry, if any, and identify the type of triangle. (Some of you may like to trace the figures and try paper folding first!)

Ans:-
(a) The given triangle is an isosceles triangle. Here it will be only 1 line of symmetry.
(b) The given triangle is an isosceles triangle. Here it will be only 1 line of symmetry.
(c) The given triangle is a right-angled triangle. Here it will be only 1 line of symmetry.
(d) The given triangle is a scalene triangle. Here it will be no line of symmetry.

Q.3. Complete the following table.

ShapeRough figureNumber of lines of symmetry
Equilateral triangleNCERT Solutions For Class 6 Maths Chapter 13 Symmetry 3
Square
Rectangle
isosceles triangle
Rhombus
Circle

Ans:-
The given table is completed as follows:

ShapeRough figureNumber of lines of symmetry
Equilateral triangleNCERT Solutions For Class 6 Maths Chapter 13 Symmetry 3
Square NCERT Solutions For Class 6 Maths Chapter 13 Symmetry4
Rectangle NCERT Solutions For Class 6 Maths Chapter 13 Symmetry2
isosceles triangle NCERT Solutions For Class 6 Maths Chapter 13 Symmetry1
Rhombus NCERT Solutions For Class 6 Maths Chapter 13 Symmetry2
Circle NCERT Solutions For Class 6 Maths Chapter 13 Symmetryinfinite

Q.4. Can you draw a triangle which has
(a) exactly one line of symmetry?
(b) exactly two lines of symmetry?
(c) exactly three lines of symmetry?
(d) no lines of symmetry?
Sketch a rough figure in each case.
Ans:-
(a) Yes, Isoscele’s right-angled triangle has exactly one line of symmetry.

(b) No, we cannot draw any triangle with two symmetric lines.
(c) Yes, an equilateral triangle has three lines of symmetry.

(d) Yes, the Scalene triangle has no lines of symmetry

Q.5. On a squared paper, sketch the following:
(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry.
(b) A quadrilateral with both horizontal and vertical lines of symmetry.
(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.
(d) A hexagon with exactly two lines of symmetry.
(e) A hexagon with six lines of symmetry.
Ans:-
(a) The figure shows an isosceles triangle with a horizontal line of symmetry.
(b) Rectangle (quadrilateral) shows both the horizontal and vertical lines of symmetry.
(c) Trapezium (quadrilateral) shows the horizontal but no vertical line of symmetry.
(d) The hexagon drawn below shows only two lines of symmetry.
(e) The regular hexagon shows the six lines of symmetry.

Q.6. Trace each figure and draw the lines of symmetry, if any:

Ans:-
(a) The given figure has no line of symmetry as it is not symmetrical.

(b) The given figure has two lines of symmetry.

(c) The given figure has four lines of symmetry.

(d) The given figure has two lines of symmetry.

(e) This figure has only one horizontal line of symmetry.

(f) The given figure has two lines of symmetry.

Q.7. Consider the letters of English alphabets, A to Z. List among them the letters which have
(a) vertical lines of symmetry (like A)
(b) horizontal lines of symmetry (like B)
(c) no lines of symmetry (like Q)
Ans:-
(a) The following letters have vertical lines of symmetry:
A, H, I, M, O, T, U, V, W, X, and Y
(b) The following letters have horizontal lines of symmetry:
B, C, D, E, H, I, K, O, and X.
(c) The following letters have no lines of symmetry:
F, G, J, L, N, P, Q, R, S, and Z.

Q.8. Given here are figures of a few folded sheets and designs drawn about the fold. In each case, draw a rough diagram of the complete figure that would be seen when the design is cut off.

Ans:-
The given figures will be seen as follows when they are completed.

NCERT Solutions For Class 6 Maths Chapter 13 Symmetry Exercises 13.3

Ch 13 Class 6 Maths Solutions ex 13.3

Q.1. Find the number of lines of symmetry in each of the following shapes. How will you check your answers?

Ans:-
(a) The given figure has 4 lines of symmetry.
(b) The given figure has only one line of symmetry.
(c) The given figure has two lines of symmetry.
(d) The given figure has two lines of symmetry.
(e) This figure has only one line of symmetry.
(f) The given figure has two lines of symmetry.

Q.2. Copy the following drawing on squared paper. Complete each one of them such that the resulting figure has two dotted lines as two lines of symmetry.

Ans:-
We can complete these figures by drawing similar parts as shown in these figures. First about the vertical line of symmetry and then about the horizontal line of symmetry or first about the horizontal line of symmetry and then about the vertical line of symmetry.
Completed figures are as follows

Q.3. In each figure alongside, a letter of the alphabet is shown along with a vertical line. Take the mirror image of the letter in the given line. Find which letters look the same after reflection (i.e. which letters look the same in the image) and which do not. Can you guess why?
Try for O E M N P H L T S V X

Ans:-
The letters having vertical lines of symmetry will have the same mirror images. These letters are O, M, H, T, V, X, and thus these letters will look the same.

Class 6 Science NCERT NotesClass 6 Complete Study Material
NCERT Solutions for Class 6 ScienceClass 6 Maths Chapter 6 Solutions

NCERT Solutions For Class 6 Maths Chapter 13 symmetry are based on NCERT Books. You can download ncert book for class 6 maths chapter 13. Ch 13 class 6 maths solutions are designed by our subject expert team.

What We Learn?

  1. A figure has line symmetry if a line can be drawn dividing the figure into two identical parts. The line is called a line of symmetry.
  2. A figure may have no line of symmetry, only one line of symmetry, two lines of symmetry or multiple lines of symmetry. Here are some examples.
Number of lines of symmetryExample
No line of symmetry
Only one line of symmetry
Two lines of symmetry
Three lines of symmetry
A scalene triangle
An isosceles triangle
A rectangle
An equilateral triangle
  1. The line symmetry is closely related to mirror reflection. When dealing with mirror reflection, we have to take into account the left ↔ right changes in orientation. Symmetry has plenty of applications in everyday life as in art, architecture, textile technology, design creations, geometrical reasoning, Kolams, Rangoli etc.