NCERT Class 6 Mathematics Chapter 9 Symmetry

NCERT Class 6 Mathematics Chapter 9 Symmetry Solutions in English Medium As Per CBSE New Syllabus to each chapter is provided in the list so that you can easily browse through different chapters NCERT Class 6 Mathematics Chapter 9 Symmetry Notes and select need one. NCERT Class 6 Mathematics Chapter 9 Symmetry Question Answers Download PDF. NCERT Class 6 Solutions for Maths in English Medium.

NCERT Class 6 Mathematics Chapter 9 Symmetry

Also, you can read the NCERT book online in these sections Solutions by Expert Teachers as per Central Board of Secondary Education (CBSE) Book guidelines. NCERT Class 6 Mathematics Chapter 9 Symmetry Textual Solutions are part of All Subject Solutions. Here we have given NCERT Class 6 Maths in English Medium Solutions. CBSE Class 6 Mathematics Textbook Solutions in English for All Chapters, You can practice these here.

Symmetry

Chapter: 9

TEXTUAL SOLUTIONS

Figure it Out (Page No. 219)

1. Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud?

Ans: (a) Yes, there are six lines of symmetry.

(b) Yes, there is one line of symmetry.

(d) There are no lines of symmetry in the picture of clouds.

2. For each of the following figures, IdentIfy the line(s) of symmetry if it exists.

Ans:

Figure it Out (Page No. 223 – 230)

1. In each of the following figures, a hole was punched in a folded square sheet of paper and then the paper was unfolded.

Identify the line along which the paper was folded.

Figure (d) was created by punching a single hole. How was the paper folded?

Ans:

2. Given the line(s) of symmetry, find the other hole(s).

Ans:

3. Here are some questions on paper cutting.

Consider a vertical fold. We represent it this way:

Similarly, a horizontal fold is represented as follows:

Ans: Do it yourself.

4. After each of the following cuts, predict the shape of the hole when the paper is opened. After you have made your prediction, make the cutouts and verify your answer.

Ans:

Ans:

Ans: Do it yourself.

Ans: Do it yourself.

5. Suppose you have to get each of these shapes with some folds and a single straight cut. How will you do it?

(a) The hole in the center is a square.

(b) The hole in the center is a square.

Note: For the above question, check if the 4-sided figures in the center satisfy both the properties of a square.

Ans: (a) By folding the square sheet along length or breadth and cutting a square at the center, we can get a square.

(b) To get the figure as shown, we fold the square diagonally and then cut the required shape in it.

6. How many lines of symmetry do these shapes have?

(i)

(ii) A triangle with equal sides and equal angles.

(iii) A hexagon with equal sides and equal sides.

Ans: (i) A diamond has 4 lines of symmetry, and the figure next to it has 4 lines of symmetry.

(ii) An equilateral triangle has three lines of symmetry.

(iii) A regular hexagon has six lines of symmetry.

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

Ans:

8. Find the lines of symmetry for the kolam below.

Ans:

9. Draw the following.

(a) A triangle with exactly one line of symmetry.

Ans:

An isosceles triangle has one line of symmetry.

(b) A triangle with exactly three lines of symmetry.

Ans:

An equilateral triangle has one line of symmetry.

(c) A triangle with no line of symmetry Is it possible to draw a triangle with exactly two lines of symmetry?

Ans:

A scalene triangle has no lines of symmetry.

No, it is not possible to draw a triangle with exactly two lines of symmetry.

10. Draw the following. In each case, the figure should contain at least one curved boundary.

(a) A figure with exactly one line of symmetry.

Ans:

(b) A figure with exactly two lines of symmetry.

Ans:

(c) A figure with exactly four lines of symmetry.

Ans:

11. Copy the following on squared paper. Complete them so that the blue line is a line of symmetry. Problem (a) has been done for you.

Hint: For (c) and (f), see if rotating the book helps!

Ans:

12. Copy the following drawing on squared paper. Complete each one of them so that the resulting figure has the two blue lines as lines of symmetry.

Ans:

13. Copy the following on a dot grid. For each figure draw two more lines to make a shape that has a line of symmetry.

Ans:

Figure it Out (Page No. 235 – 236)

1. Find the angle of symmetry for the given figures about the point marked.

Ans: (a) 90°

(b) 360°

2. Which of the following figures have more than one angle of symmetry?

Ans:

The given figure comes back to its original shape when we rotate it about 90°, 180°, 270° and 360°. Thus, the given figure has 4 angles of symmetry (90°, 180°, 270° and 360°).

The figure comes back to its original shape only after 360° rotation. So, the figure has only one angle of symmetry i.e., 360°.

The given figure comes back to its original shape when we rotate it about 120°, 240° and 360°. Thus, the given figure has 3 angles of symmetry (120°, 240° and 360°).

The given figure comes back to its original shape when we rotate it about 90°, 180°, 270° and 360°. Thus, the given figure has 4 angles of symmetry (90°, 180°, 270° and 360°).

The given figure comes back to its original shape when we rotate it about 90°, 180°, 270° and 360°. Thus, the given figure has 4 angles of symmetry (90°, 180°, 270° and 360°).

The given figure comes back to its original shape when we rotate it about 72°, 144°, 216°, 288° and 360°. Thus, the given figure has 5 angles of symmetry (72°, 144°, 216°, 288° and 360°).

The given figure comes back to its original shape when we rotate it about a complete turn, i.e., at 360°. Thus, the figure does not have

3. Give the order of rotational symmetry for each figure:

Ans:

Figure it Out (Page No. 238)

1. Color the sectors of the circle below so that the figure has:

(a) 3 angles of symmetry.

(b) 4 angles of symmetry.

(c) what are the possible numbers of angles of symmetry you can obtain by coloring the sectors in different ways?

Ans: (a) Will look same after every rotation of 120°.

(b) Will look same after every rotation of 90°.

2. Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry.

Ans:

3. Draw wherever possible, a rough sketch of:

(a) a triangle with atleast two lines of symmetry and atleast two angles of symmetry.

(b) a triangle with only one line of symmetry but not having rotational symmetry.

(c) a quadrilateral with rotational symmetry but no reflection symmetry.

(d) a quadrilateral with reflection symmetry but not having rotational symmetry.

Ans:

4. In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?

Ans: It will also look the same by rotating at an angle of 120°, 180°, 240°, 300°, and 360° as these are the multiples of 60°.

5. In a figure, 60° is an angle of symmetry. The figure has two angles of symmetry less than 60°. What is its smallest angle of symmetry?

Ans: Smallest angle of symmetry = 60° ÷ 3 = 20°.

6. Can we have a figure with rotational symmetry whose smallest angle of symmetry is:

(a) 45 °?

(b) 17°?

Ans: (a) Since, the complete rotation is 360°. Then, if the given angle divides 360°, it can be an angle of symmetry.

Here, 360∘/45∘ = 8, which is a whole number.

Therefore, 45° can be the smallest angle of symmetry of a figure.

(b) Here, 360∘/17∘ = 21 3/17, which is not a whole number.

Therefore, 17° cannot be the smallest angle of symmetry.

7. This is a picture of the new Parliament Building in Delhi.

(a) Does the outer boundary of the picture have reflection symmetry? If so, draw the lines of symmetries. How many are they?

(b) Does it have rotational symmetry around its centre?

If so, find the angles of rotational symmetry.

Ans: (a) Let us label the given figure and check whether its one side overlaps the other side when folded about the dotted line drawn in the middle of the figure.

We observes that one half covers exactly the other half. Thus, it has a reflection symmetry.

Lines of symmetry:

There are three lines of symmetry.

(b) The given figure has rotational symmetry around its centre.

When we rotate it about 120°, 240° and 360°, we get the original shape. Thus, the angles of rotational symmetry are 120°, 240° and 360°.

8. How many lines of symmetry do the shapes in the first shape sequence in Chapter 1, Table 3, the Regular Polygons, have? What number sequence do you get?

Ans: Do Yourself

9. How many angles of symmetry do the shapes in the fist shape sequence in Chapter 1, Table 3, the Regular Polygons, have? What number sequence do you get?

Ans: Number of angles of symmetry = number of lines of symmetry.

Hence we get the number sequence: 3, 4, 5, 6, 7, ………..

10. How many lines of symmetry do the shapes in the first shape sequence in Chapter 1, Table 3, the Koch Snowflake sequence, have? What angle of symmetry?

Ans: