CBSE Important Questions Class 6 Maths Chapter 9 – Symmetry
Class 6 Maths Chapter 9 Symmetry is part of the new NCERT textbook Ganita Prakash. It teaches students what symmetry means and how to find it in shapes around us. Students learn about lines of symmetry (reflection symmetry) using paper folding and cutting, how to complete a figure so that it becomes symmetrical, and rotational symmetry, where a shape looks the same after a turn, along with the order and angle of rotational symmetry.
These CBSE important questions for Class 6 Maths Chapter 9 cover predicting the hole made by cuts on folded paper, getting a square hole with folds and a single cut, drawing lines of symmetry on figures, completing drawings on squared and dot grids, rotational symmetry of a regular hexagon and pentagon, and assertion-reason questions on angles of symmetry. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them for class tests. A free printable PDF of these important questions is also available on this page.
CBSE Important Questions Class 6 Maths Chapter 9 – Symmetry
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Q1. 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.
(a)
(b)
(c)
(d)
Answer: The fold line works as a line of symmetry, so the cut is mirrored on the other side when the paper is opened.
(a) The wavy cut on the folded edge opens into one symmetrical wavy hole in the middle of the paper.
(b) The zigzag cut is mirrored across the fold and opens into a symmetrical banner-like hole.
(c) The paper was folded twice, so the corner cut appears four times, once in each quarter, giving the shape shown.
(d) The two rectangular cuts are mirrored across the fold, giving two wide notches at the top and bottom and a square hole in the centre.
Q2. 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 centre is a square.
(b) The hole in the centre is a square.
Note: For the above two questions, check if the 4-sided figures in the centre satisfy both the properties of a square.
Answer: (a) Fold the paper in half, then fold it in half again so that all four corners meet at the centre of the paper. Now make one straight cut across the folded corner. When you open the paper, a square hole appears in the centre with its sides parallel to the edges of the paper.
(b) Fold the paper in half twice in the same way, then fold the corner once more along the diagonal. A single straight cut through the folded corner now opens into a square hole turned by 45°, which looks like a diamond.
In both cases the hole has four equal sides and four right angles, so it is a square.
Q3. Trace each figure and draw the lines of symmetry, if any:
Answer: The lines of symmetry are shown below.
Figure 1 (three diamonds stacked up and down): 1 line of symmetry (vertical).
Figure 2 (three diamonds in a row): 1 line of symmetry (horizontal).
Figure 3 (four diamonds forming a bigger diamond): 4 lines of symmetry (vertical, horizontal and two diagonals).
Figure 4 (four diamonds in a cross): 2 lines of symmetry (vertical and horizontal).
Figure 5 (square): 4 lines of symmetry.
Figure 6 (hexagon on the grid): 2 lines of symmetry (vertical and horizontal).
Figure 7 (the kite-like shape): 1 line of symmetry (horizontal).
Figure 8 (four-pointed star): 4 lines of symmetry.
Q4. 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.
Answer: To complete each figure, reflect the red part across the first blue line, and then reflect everything across the second blue line. The completed figures are shown below.
(a) becomes a square, (b) an eight-pointed star shape, (c) a stepped rectangle, (d) an octagon, (e) a plus-shaped figure with pointed ends, and (f) a double bow-tie shape.
Q5. Copy the following on a dot grid. For each figure draw two more lines to make a shape that has a line of symmetry.
Answer: Choose a line of symmetry (vertical for the first five figures, horizontal for the last one) and draw the mirror image of the given lines on the other side. The two new lines (shown in pink) complete each shape so that it has one line of symmetry.
Q6. Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry.
Answer: An oval (ellipse) and a rectangle.
An oval has 2 lines of symmetry and looks the same after a half turn (180°), so it has rotational symmetry of order 2.
A rectangle also has 2 lines of symmetry and rotational symmetry of order 2.
Q7. Symmetry plays an important role in geometry, art, and nature, and it's helpful to classify shapes based on their symmetrical properties. By answering the following questions, you will gain a deeper understanding of how symmetry works in various shapes.
(i) Draw a triangle with three lines of symmetry.
(ii) Draw a hexagon with six lines of symmetry.
(iii) Draw a triangle with no line of symmetry.
Answer: (i) An equilateral triangle (all three sides equal) has 3 lines of symmetry.
(ii) A regular hexagon (all six sides equal) has 6 lines of symmetry.
(iii) A scalene triangle (all three sides different) has no line of symmetry.
Q8. Kajol decided to use a regular hexagon (a six-sided polygon where all sides and angles are equal) for her design, as she had recently learned about the symmetry of different shapes in her geometry class. Kajol was fascinated by how a simple shape could look the same after a series of transformations. She began to investigate how the regular hexagon behaved under rotations and reflections, wondering if her design would hold up when tiles were shifted or flipped.
(i) Does the regular hexagon have rotational symmetry? If yes, what is the smallest angle of rotation?
(ii) What is the order of rotation for a regular hexagon?
(iii) Does the regular hexagon have reflection symmetry? If yes, how many lines of symmetry does it have? Illustrate your answer with a diagram.
Answer: (i) Yes. The smallest angle of rotation is 360° ÷ 6 = 60°, because the hexagon looks the same after turning through 60°.
(ii) The order of rotational symmetry of a regular hexagon is 6 (it looks the same 6 times in one full turn).
(iii) Yes, the regular hexagon has reflection symmetry. It has 6 lines of symmetry: 3 through opposite corners and 3 through the midpoints of opposite sides.
Q9. Assertion: A circle has infinite angles of symmetry.
Reason: A circle can be rotated by any angle around its center and still appear the same.
(a) Both Assertion and Reason are true, and the Reason is the correct explanation for the Assertion.
(b) Both Assertion and Reason are true, but the Reason is not the correct explanation for the Assertion.
(c) Assertion is true, but Reason is false.
(d) Assertion is false, but Reason is true.
Answer: (a) Both Assertion and Reason are true, and the Reason is the correct explanation for the Assertion.
A circle looks exactly the same after rotating it about its centre by any angle (1°, 2°, 45°, 90° and so on). Since every angle works, there are infinitely many angles of symmetry. The Reason states exactly this property, so it explains the Assertion.
Q10. Assertion: A hexagon with non-equal sides has six angles of symmetry.
Reason: A regular polygon (all sides equal) with n sides has n angles of symmetry.
(a) Both Assertion and Reason are true, and the Reason is the correct explanation for the Assertion.
(b) Both Assertion and Reason are true, but the Reason is not the correct explanation for the Assertion.
(c) Assertion is true, but Reason is false.
(d) Assertion is false, but Reason is true.
Answer: (d) Assertion is false, but Reason is true.
Only a regular hexagon (all sides and angles equal) has six angles of symmetry. A hexagon with unequal sides has fewer, often none. So the Assertion is false.
A regular polygon with n sides has n angles of symmetry (a square has 4, a regular pentagon has 5, a regular hexagon has 6). So the Reason is true.
Q11. Five sticks are arranged in the form of a regular pentagon shape. If we rotate the figure about a fixed point, how many positions are there at which the figure looks exactly the same? Also, find the angle of rotational symmetry.
Answer: A regular pentagon has 5 equal sides, so in one full turn there are 5 positions at which the figure looks exactly the same.
So the order of rotational symmetry is 5.
Angle of rotational symmetry = 360° ÷ order of rotational symmetry = 360° ÷ 5 = 72°
Q12. Show the line of symmetry in equilateral triangle, isosceles triangle and scalene triangle.
Answer: 1. An equilateral triangle has 3 lines of symmetry.
2. An isosceles triangle has 1 line of symmetry.
3. A scalene triangle has no line of symmetry.
Related Study Material on Extramarks
- CBSE Important Questions Class 6 Maths Chapter 1
- CBSE Important Questions Class 6 Maths Chapter 2
- CBSE Important Questions Class 6 Maths Chapter 3
- CBSE Important Questions Class 6 Maths Chapter 4
- CBSE Important Questions Class 6 Maths Chapter 5
- CBSE Important Questions Class 6 Maths Chapter 6
- CBSE Important Questions Class 6 Maths Chapter 7
- CBSE Important Questions Class 6 Maths Chapter 8
- CBSE Important Questions Class 6 Maths Chapter 10
Q.1 Read the bar graph given below which shows the number of new players enrolled in different years in a cricket academy.
Identify the years in which number of enrollments are in the ratio 2:3.
A. Years 2017 and 2015
B. Years 2016 and 2018
C. Years 2018 and 2015
D. Years 2016 and 2017
Marks:1
Ans
From the given bar graph, we find that the number of players enrolled in years 2015, 2016, 2017 and 2018 are 30, 40, 50 and 60 respectively.
Given ratio = 2 : 3 = 40 : 60
Required years are 2016 and 2018.
Q.2 The following pictograph shows the number of varieties of apples stored in a supermarket. The total number of apples stored in the supermarket is:
A. 150
B. 100
C. 50
D. 16
Marks:1
Ans
150
The pictograph shows 14 full and 2 half apples.
Thus, the total number of apples stored in the supermarket
= (14 x 10) + (2 x 5) = 140 + 10 = 150 apples
Q.3 The following bar graph shows the number of houses in a village using different types of fuels for cooking.
Which of the following are the two fuels that are used by half of the total houses in the village?
A. LPG and coal
B. wood and coal
C. LPG and kerosene
D. wood and kerosene
Marks:1
Ans
Total houses = 1000
Half of the total houses = 1000/2 = 500
Number of houses that use wood = 250
Number of houses that use kerosene = 250
Number of houses that use wood and kerosene
= 250+250 = 500
No other two fuels are used by half of the total houses in the village.
Q.4 The number of English books sold by a shopkeeper on six consecutive days is shown below:
| Days | Monday | Tuesday | Wednesday | Thursday | Friday |
| Number of Books Sold | 60 | 55 | 50 | 45 | 30 |
Draw a bar graph to represent the above information choosing the scale of your choice.
Marks:4
Ans
Q.5 The weights of 25 students of a class are given below, prepare a frequency chart.
44 kg, 46 kg, 39 kg, 41 kg, 45 kg
34 kg, 36 kg, 49 kg, 43 kg, 35 kg
43 kg, 42 kg, 37 kg, 34 kg, 38 kg
40 kg, 42 kg, 45 kg, 46 kg, 47 kg
41 kg, 48 kg, 47 kg, 40 kg, 41 kg
| Class Interval | Tally Marks | Number of Students | ||||||||||||||
| 30-35 | 2 | |||||||||||||||
| 35-40 | 5 | |||||||||||||||
| 40-45 | 10 | |||||||||||||||
| 45-50 | Marks:2Ans
|
FAQs (Frequently Asked Questions)
Symmetry means a figure has parts that repeat in a definite pattern. A figure may show this through folding, reflection or rotation.
A line of symmetry divides a figure into two parts that overlap exactly when folded. A square has four lines of symmetry.
Rotational symmetry means a figure looks the same after rotation about a fixed point. A square has rotational symmetry at 90°, 180°, 270° and 360°.
A rectangle has two lines of symmetry. They pass through the centre vertically and horizontally.
Reflection symmetry uses a mirror line to match two halves. Rotational symmetry uses a turn around a fixed centre to match the figure.