CBSE Important Questions Class 6 Maths Chapter 13

Important Questions Class 6 Maths Chapter 13 – Symmetry

Maths is a major subject that is taught in school. It has wide applications in our life. Everyone uses Maths to solve real-life problems, from shop owners to engineers.

Chapter 13 of Class 6 Maths is about symmetry. Symmetry is a property of an object. The property of getting divided into two perfect halves along an axis is called symmetry. An object that can be divided into two identical halves along a line is called a symmetrical object. If the object doesn’t have this property, it is called asymmetrical. It is a new concept for students, and they should practice questions from this chapter to build their concepts.

Extramarks is a leading company that provides students with a wide range of study materials. Our experts made the Important Questions Class 6 Maths Chapter 13, collected the questions from different sources, and provided the answers. Students may solve the questions to score better in exams.

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Important Questions Class 6 Maths Chapter 13 – With Solutions

The experts of Extramarks have collated the questions from several sources like the textbook exercise, NCERT exemplar, CBSE past years’ question papers, CBSE sample papers and different reference books. Apart from this, they have solved the questions. Experienced professionals have checked the answers to ensure the best quality of content for students. Students may follow the Important Questions Class 6 Maths Chapter 13 to score better in exams. The questions are-

Question 1 List any four of the symmetrical objects from your home or school.

Answer 1-

The following objects can be symmetrical:

(a) Notebook

(b) Dining table

(c) A blackboard

(d) Wall clock

(e) A pair of scissors

Question 2 The symmetrical number of lines present in a scalene triangle is

(i) 0

(ii) 1

(iii) 2

(iv) 3

Answer 2:

(i) A scalene triangle contains no line of symmetry present in it.

Question 4. The number of lines present in a circle is

(i) 0

(ii) 2

(iii) 4

(iv) more than 4

 Answer 4

(iv) Since a circle is a symmetrical figure, about each of its diameters, thus, every diameter of a circle is considered an axis of symmetry.

Question 5.

The instrument sent in the geometry box having the shape of a triangle is called?

(i) Protractor

(ii) Compass

(iii) Divider

(iv) Set-square

Answer 5:

(iv) The instrument set square in the geometry box has the shape of a triangle.

Question 6. The instrument used to measure an angle is a

(i) Ruler

(ii) Protractor

(iii) Divider

(iv) Compass

Answer 6:

(ii) The instrument called a protractor is used to measure an angle.

Question 7.

The instrument to draw a circle is

(i) Ruler

(ii) Protractor

(iii) Divider

(iv) Compass

Answer 7:

(iv) The instrument compass is used to draw a circle.

Question 8 For the given figure, which of the following ones is the mirror line, l1 or l2?

Answer 8:

In the following figure, l2 is the mirror line.

Question 9. Copy the following diagram on squared paper. A square paper is what you would have used in your arithmetic notebook in your earlier classes. Then complete the figures such that the dotted line is the line of symmetry.
Answer 9:

Question 10. In the figure, l is called a line of symmetry. Complete the diagram to make it symmetric.

Answer 10. The completed figure is as follows:

Question 11. In the figure, l is called the line of symmetry. Draw the image of the triangle and then complete the diagram so that it becomes symmetrical in nature.

Answer 11

The symmetric figure is given as follows.

Question 12. Can you draw a triangle which contains

(i) exactly one line of symmetry?

(ii) exactly two lines of symmetry?

(iii) exactly three lines of symmetry?

(iv) no lines of symmetry?

Sketch a rough figure in each case.

Answer 12

(i) Yes, Isosceles’ right-angled triangle has exactly one line of symmetry.

(ii) No, we cannot draw any triangle with two symmetric lines.

(iii) Yes, an equilateral triangle has three lines of symmetry.

(iv) Yes, the scalene triangle has no lines of symmetry
Question 13. On a squared paper, sketch the following statements given below:

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

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

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

(iv) A hexagon with exactly two symmetrical lines.

(v) A hexagon with six lines of symmetry. (Hint point: It will be helpful if you first draw the lines of symmetry and then complete the figures)

Answer 13

(i) The figure shows an isosceles triangle with a horizontal line of symmetry.

(ii) Rectangle (quadrilateral) shows both the horizontal and vertical lines of symmetry.

(iii) Trapezium (quadrilateral) shows the horizontal but no vertical line of symmetry.

(iv) The hexagon drawn below shows only two lines of symmetry.

(v) The regular hexagon shows the six lines of symmetry.

Question 14. Consider the letters of English alphabets from A to Z. List among them the letters which contain

(i) vertical lines of symmetry (like A)

(ii) horizontal lines of symmetry (like B)

(iii) no lines of symmetry (like Q)

Answer 14

(i) These following letters have vertical lines of symmetry present in them:

Letter A, H, I, M, O, T, U, V, W, X, and Y

(ii) The following letters have horizontal lines of symmetry present in them:

 Letter B, C, D, H, E, I, K, O and X.

(iii) The following letters have no lines of symmetry present in them:

Letter F, G, J, L, N, P, Q, R, S and Z.

Question 15. In the given figure, point C is the image of point A inline l, and line segment BC intersects line l at P.

(i) Is the image of P in line l known as the point P itself?

(ii) Is PA = PO

(iii) Is PA + PB = PC + PB?

(iv) Is P that point on line l from which the sum of the distances of points A and B is minimum?

Answer 15

(i) Yes 

(ii) Yes 

(iii) Yes

Since, PA = PC

⇒ PA + PB = PC + PB

[By adding PB on both sides]

(iv) Yes, since, PA + PB = CP + PB

Now, CP + PB will be the minimum when C, P and B lie on a line.

Question 16. Find the number of lines of symmetry present in each of the following shapes. How will you check your answer?
Answer 16

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

(ii) The given figure has only one line of symmetry.

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

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

(v) This figure has only one line of symmetry.

(vi) The given figure has two lines of symmetry.
Question 17. The symmetrical number of lines present in a rectangle and a rhombus is ____ (equal or unequal).

Answer 17

Equal because both rectangle and rhombus have two lines of symmetry.

Question 18. The symmetrical number of lines present in a rectangle and a square is ___ (equal or unequal).

Answer 18

Unequal because A rectangle has two lines of symmetry, and a square has four lines of symmetry.

Question 19. If a line segment of 5 cm length is reflected in the line of symmetry of amirror, then its reflection (image) is a ___ of length ____.

Answer 19

Line segment, 5 cm

Question 20. Find the number of lines of symmetry present in each of the following shapes.

Answer 20

(i) Here, there are four symmetric lines l, m, n and o.

(ii) In this figure, there are four symmetric lines p, q, r and s.

(iii) In this shape, u, v , w and x are four lines of symmetry.

(iv) In this shape only m is the line of symmetry.

(v) Here, a, b, c, d, e and fare six lines of symmetry.

(vi) In this figure l, m, n, o, p and q are six lines of symmetry.

(vii) This figure has no lines of symmetry.

(viii) This figure has no lines of symmetry.

(ix) This figure has five lines of symmetry.

Question 21. Identify the shapes given below. Also, Check whether they are symmetrical or not. Draw the line of symmetry as well.
Answer 21

(i) The given symmetric figure is a lock in which vertical line ‘l’ is the line of symmetry.

(ii) The given figure is a symmetrical bucket in which vertical line ‘l’ is the line of symmetry.

(iii) The given figure is not symmetrical.

(iv) The given figure is a symmetric telephone in which vertical line l is called the line of symmetry.

(v) The given figure is symmetrical. Horizontal line l is called the line of symmetry.

(vi) The given figure is symmetrical. Vertical line l is called its line of symmetry.

Question 22. A rhombus is symmetrical about its  ____.

Answer 22

Diagonals

Question 23.

A rectangle is only symmetrical about the lines joining the ___ of the opposite sides.

Answer 23

Midpoints

Question 24 A right triangle contains at most one line of symmetry. State whether the statement is true or false.

Answer 24

The statement is true.

A right triangle contains at most one line of symmetry if its remaining two angles are equal.

Question 25.  A kite has two lines of symmetry.

Answer 25

False

Because a kite only has one line of symmetry.

Question 26 .

A parallelogram contains no line of symmetry.

Answer 26

True

Question 27

If an isosceles triangle contains more than one line of symmetry, then will it be an equilateral triangle?

Answer 27

False

Since the isosceles triangle is symmetrical about its bisector of the angle, the angle includes between the equal sides, which is only one line of symmetry.

∴ If it contains more than one line of symmetry, then it must be considered an equilateral triangle.

Question 28

If a rectangle contains more than two lines of symmetry, then it will be a square.

Answer 28

True

Question 29. Which of the following letters do not have the vertical line of symmetry present in them?

(i) M

(ii) H

(iii) E

(iv) V

Answer 29

Above letters show that E is the only letter which has no vertical line of symmetry.

Question 30

Which of the following letters contain both horizontal and vertical lines of symmetry?

(A) X

(B) E

(C) M

(D) K

Answer 30

The above letters show that X has both horizontal and vertical line of symmetry, E and K has horizontal line of symmetry, and M has a vertical line of symmetry.

Question 31.

Which of the following letters does not contain any line of symmetry?

(A) M

(B) S

(C) K

(D) H

Answer 31
The above letters show that letter S has no lines of symmetry present in them.

Question 32.

Which of the following letters contain only one line of symmetry?

(A) H

(B) X

(C) Z

(D) T

Answer 32
The above letters show that letters H and X have both vertical and horizontal lines of symmetry, while the letter Z has no line of symmetry, and the letter T has only one (horizontal) line of symmetry.

Question 33. Complete the following figure, so that line l becomes the line of symmetry of the whole figure.

Answer 33n>https://www.learncbse.in/ncert-exemplar-class-6-Mathematics-chapter-9/

Question 34.

Draw the images of points A, B and C in the line as m. Describe them as A’, B’ and C’, respectively and then join them in pairs. Also, measure lines AB, BC, CA, A’B’, B’C’ and CA’. Find whether AB = A’B’, BC = B’C’ and CA = C’A’?

Answer 34

Yes, the line AB = A’B’, BC = B’C’ and CA = CA’

Question 35. Copy the triangle present in each of the figures on squared paper. In every case, draw the line(s) of symmetry and then identify the type of triangle. (You may want to trace the figures and try the paper-folding method first!)

Answer 35

(a) It is an isosceles triangle containing only one symmetric line.

(b) This figure is also an isosceles triangle containing only one symmetric line.

(c) It is also an isosceles right angled triangle which has only one symmetric line.

(d) It is a scalene triangle. It has no symmetric line.

Question 36. Trace each of the figures and draw the lines of symmetry present in them.

Answer 36

(i) The given figure has no line of symmetry as it is not symmetrical.

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

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

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

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

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

Question 37. Given here are different figures of a few folded sheets and designs drawn about the folds of the sheet. In each case, draw a complete rough diagram of the complete figure given below so that it would be observed when the design is removed.
Answer 37:

The given figures, when completed, will be seen as follows.
Question 38.

Draw the images of P’, Q’ and R’ with the points P, Q and R, respectively, in the line n (see the figure given below). Join the P’Q’ and Q’R’ to form an angle P’Q’R’. Measure ∠QPR and ∠P’Q’R’. Are the two angles equal?
Answer 38
Yes, ∠PQR and ∠P’Q’R’

Question 39.

Complete the following figure by taking l as the line of symmetry of the whole figure.

Answer 39
Question 40

A 30° – 60° – 90° set-square contains how many lines/lines of symmetry.

Answer 40:

No, it doesn’t ave any line of symmetry.

Question 41

A 45° – 45° – 90° set-square contains how many lines/lines of symmetry.

Answer 41:

It has one line of symmetry.

 Question 42

The symmetrical number of lines present in a 45° – 45° – 90° set-square is

(i) 0

(ii) 1

(iii) 2

(iv) 3

Answer 42:

(ii) The set-square of measurement present in 45° – 45° – 90° is in the shape of an isosceles right-angled triangle which contains one line of symmetry.

 Question 43 .-

The symmetrical number of lines present in a 30° – 60° – 90° set of a square is

(i) 0

(ii) 1

(iii) 2

(iv) 3

Answer 43:

(i) The set-square of measurement of 30 ° – 60° – 90° is in the shape of a scalene right-angled triangle which contains no line of symmetry.

Benefits of Solving Important Questions Class 6 Maths Chapter 13

Students must practice as much as possible to clear their doubts. Practice helps them to boost their confidence. Thus, practice is important for higher marks in exams. The concept of symmetry is a new concept to students. So, they must solve different questions from the chapter to build their ideas. They will need the concepts in higher classes too. So, they may follow the Important Questions Class 6 Maths Chapter 13 prepared by the experts of Extramarks. They will have several benefits for solving the questions. These are-

• The textbook exercise is not enough for students to practise. So they have to take help from other sources. Now, this is tiresome for students to search for different questions in different books. Our experts have done the task for them. They have collected the questions from several sources, such as CBSE sample papers, CBSE past years’ question papers, NCERT exemplar and reference books. Thus, students will find all the possible types of questions from the chapter in the Chapter 13 Class 6 Maths Important Questions.
• The experts have also solved the questions. They have given a step-step solution to each question. Thus, the students can take help from the keys if they have doubts. They can also tally their answers with the solutions. Experienced professionals have further checked the answers to ensure students’ best content quality. Thus, the Maths Class 6 Chapter 13 Important Questions will also help the students solve different questions.
• Students should solve different questions to build practice habits because practice is very important and will help students in many ways. It will help them clear their doubts and build the chapter’s concepts. It will also boost their confidence which will help them to score higher in the exams. Thus, the Class 6 Maths Chapter 13 Important Questions will help students save time, boost confidence and increase exam marks.

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