NCERT Solutions for Class 4 Maths Mela Chapter 11 Fun with Symmetry

Question 1. Is it a symmetrical pattern? Where would you draw the line that divides this design into two equal halves?
Answer: Yes, this is a symmetrical pattern. When you fold the paper and spread color on it, the design on one half becomes a mirror copy of the design on the other half when you open it. Both halves match in shape and size. A vertical line through the middle of the design, along where the paper was folded, divides it into two equal and matching parts. This pattern has one line of symmetry, which is the vertical line at the centre.
In simple words: The design looks the same on both sides of a middle line. The middle line is vertical and splits the design perfectly in half.

Exam Tip: When identifying symmetry, look for a fold line where one side mirrors the other side exactly. Count the lines carefully - this design has one line of symmetry only.

Question 2. Is it a symmetrical pattern? Where would you draw the line that divides this design into two equal halves?
Answer: Yes, this is a symmetrical pattern. When you fold the paper and spread colour on it, the design on one half becomes a mirror copy of the design on the other half when you open it. Both halves match in shape and size. A vertical line through the middle of the design, along where the paper was folded, divides it into two equal and matching parts. This pattern has one line of symmetry, which is the vertical line at the centre.
In simple words: The design looks the same on both sides of a middle line. The middle line is vertical and splits the design perfectly in half.

Exam Tip: When identifying symmetry, look for a fold line where one side mirrors the other side exactly. Count the lines carefully - this design has one line of symmetry only.

Question 3. Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.
Answer: Lines of symmetry have been marked in red (dashed lines) on all three figures. Fig. 3 shows a vertical line through the middle. Fig. 4 shows a horizontal line across the middle. Fig. 5 shows a vertical line down the centre.
In simple words: Draw a line where each shape would fold in half with matching parts on both sides.

Exam Tip: The line of symmetry can be vertical, horizontal, or diagonal. Always check that both sides match perfectly when folded along this line.

Question 4. How many lines of symmetry can you see in Fig. 8?
Answer: One line of symmetry can be seen in Fig. 8. This line runs vertically down the middle of the fan-shaped design.
In simple words: The shape has only one line where you can fold it and have both halves match.

Exam Tip: Count the lines by checking each possible fold direction - vertical, horizontal, and diagonal. Only count lines where the two parts are exactly the same.

Question 5. Where will you place a mirror to see the reflection of the right half side of Fig. 8? Will it look the same as the left half side?
Answer: Place the mirror along the vertical line of symmetry running down the middle of the shape. Yes, the reflection of the right half will look exactly the same as the left half if the shape is perfectly symmetrical. The mirror will show you that both halves are identical copies of each other.
In simple words: Put the mirror down the middle line. The right side's reflection will match the left side perfectly.

Exam Tip: The mirror must be placed exactly on the line of symmetry. If positioned correctly, one half and its mirror image create the complete shape.

Question 6. Fly the plane.
Answer: Do this activity yourself. Test how the paper aeroplane flies when it has symmetrical folds.
In simple words: Make a paper plane and throw it to see if it flies straight.

Exam Tip: Observe whether the plane flies in a straight line or curves to one side, then record your observations.

Question 7. Will the plane fly if there is no line of symmetry?
Answer: If a paper aeroplane has no line of symmetry, it will not fly straight. Instead, it will tend to curve or spin toward the larger side. This happens because the two wings are not balanced.
In simple words: Without symmetry, the plane will not fly straight - it will move sideways or spin.

Exam Tip: The more uneven the two sides are, the more the plane will curve or drop. Symmetry helps balance the aeroplane.

Question 8. Try to make an asymmetrical plane.
Answer: Create an asymmetrical plane by folding one wing bigger than the other. Now the plane has no line of symmetry. You can compare this to a symmetrical plane to see the difference.
In simple words: Fold one wing bigger than the other to make a plane that is not balanced.

Exam Tip: Make clear differences between the two wings so you can clearly observe the effects of asymmetry.

Question 9. Fly both the planes and see which plane flies for a longer time.
Answer: The symmetrical plane flies straighter and for a longer time. The asymmetrical plane flies for a shorter time and may move sideways or fall early. This shows that balance and symmetry help objects fly better.
In simple words: The balanced plane stays in the air longer than the unbalanced one.

Exam Tip: Time both planes carefully and note how far they travel. The symmetrical plane should outperform the asymmetrical one in both distance and duration.

Question 10. Share your observations with your friends.
Answer: I observed that the plane with a line of symmetry flew straight and stayed in the air longer. The asymmetrical plane did not fly well and fell quickly. So, symmetry helps a plane fly better. Symmetrical objects are more balanced, which makes them move smoothly through the air.
In simple words: When both sides match, the plane flies better and longer.

Exam Tip: When sharing observations, describe what you saw, explain why it happened (because of symmetry), and draw a conclusion about the importance of balance.

Question 11. Where would the hole and cut appear when you open the paper?
Answer: When Rani's paper is opened, the straight cut at the corner will create a V-shaped notch in the middle of one edge. One square cut becomes a rectangle. The other square cut will show up as two squares, placed symmetrically on the paper. Both holes and cuts mirror each other because the paper was folded.
In simple words: The holes and cuts appear twice - once on each side of the fold line, mirroring each other.

Exam Tip: Remember that when you cut or punch a folded paper, the mark appears on both layers. When unfolded, you see a symmetrical pattern of holes and cuts.

Question 12. Fold a piece of paper once; put two cuts in the middle as shown. How many sides will this shape have when you open the folded paper?
Answer: When opened, a rhombus will appear. A rhombus is a four-sided shape with all sides of equal length. The two cuts on the folded paper create this four-sided figure with a symmetrical appearance.
In simple words: The shape that opens up is a rhombus, which has four equal sides.

Exam Tip: Predict the final shape before unfolding by thinking about how cuts on folded paper will mirror on both sides.

Question 13. Fold a paper twice. Where would you cut to make a square hole in the centre of the paper? How many cuts are required?
Answer: To make a square hole in the center, you need to cut a square at the point where all folds meet. You need only 1 cut to create a square hole in the center. Since the paper is folded twice, this single cut will go through four layers of paper, making the hole appear four times when unfolded - once in the center of each quarter.
In simple words: Make one cut at the center where the folds cross. When you open the paper, you get a square hole in the middle.

Exam Tip: When paper is folded multiple times, one cut creates multiple identical marks. Think about the layers when planning your cut.

Question 14. Complete the designs below.
Answer: The completed designs show symmetrical patterns. Each design has been filled in on the blank side to match the side shown. The patterns on both sides of the line of symmetry are identical and mirror each other perfectly.
In simple words: Draw the same pattern on the blank side so both halves look exactly alike.

Exam Tip: Use the line of symmetry as your guide. Every point on one side should have a matching point on the other side at the same distance from the line.

Question 15. Look at the shapes given along the border. Draw these shapes on the dot grid. Which of the shapes are symmetrical? Draw the lines of the symmetry.
Answer: When drawn on the dot grid, the rectangle and the arrow shape are symmetrical. The kite and the rectangle have vertical lines of symmetry. The rectangle has two lines of symmetry - one vertical and one horizontal. The arrow has one vertical line of symmetry. The irregular shape is not symmetrical and has no line of symmetry.
In simple words: Some shapes can be folded in half with matching sides. These shapes are symmetrical and have lines of symmetry.

Exam Tip: Check each shape by testing if it folds perfectly along different lines. Count each line of symmetry carefully - some shapes have more than one.

Question 16. Where should we place the mirror in shape A to get the shapes given below?
Answer: To get shape 1 (a square), place the mirror vertically at the centre. To get shape 2 (a rectangle), place the mirror horizontally at the centre. To get shape 3 (an L-shape), place the mirror diagonally. To get shape 4 (a rectangle), place the mirror vertically. To get shape 5 (a complete shape), place the mirror vertically through the middle. To get shape 6 (a long rectangle), place the mirror vertically at the centre.
In simple words: The mirror position changes the reflected shape. Different mirror placements create different final shapes.

Exam Tip: The direction you place the mirror (vertical, horizontal, or diagonal) determines which shape you will see in the reflection.

Question 17. Circle the numbers whose mirror image is the same number.
Answer: The numbers 181, 686 should be circled. These numbers look the same when a vertical mirror is placed in the middle of them.
In simple words: Circle the numbers that look the same when you put a mirror down their middle.

Exam Tip: Check each number by imagining a vertical mirror line running through its centre. Only numbers where both halves are mirror images of each other should be circled.

Question 18. Which digits from 0 to 9 have the same mirror image?
Answer: The digits that have the same mirror image are 0, 1, and 8. These three digits look identical when reflected in a mirror, whether the mirror is placed vertically or horizontally. All other digits (2, 3, 4, 5, 6, 7, 9) have mirror images that look different from the original digit.
In simple words: Only 0, 1, and 8 look the same in a mirror. All other digits look different.

Exam Tip: Test each digit by drawing it and checking what its mirror image looks like. The digits 0, 1, and 8 have perfect vertical symmetry.

Question 19. Make some 4-digit numbers such that the mirror image is the same number. Where would you keep the mirror in each case? How many such numbers can you make?
Answer: Some correct examples are 1001, 1111, 1881, 8008, 8118, and many more. All these numbers look the same when a mirror is placed vertically in the middle or horizontally below the number. The mirror should be kept vertically between the 2nd and 3rd digit. You can also place the mirror below the number. Many such numbers can be made, because the 1st and 4th digits must be the same, the 2nd and 3rd digits must be the same, and you can choose from 0, 1, and 8. So, there are several such mirror numbers possible.
In simple words: Use only 0, 1, and 8. Make the first and last digits match, and make the middle two digits match.

Exam Tip: Systematic counting helps: first digit (3 choices: 0, 1, 8), second digit (3 choices: 0, 1, 8), then the middle two repeat these. This gives 3 × 3 = 9 possible numbers.

Question 20. Make similar questions and ask your friends to guess the numbers.
Answer: Guess My Number - Question 1: My number is a 4-digit number. Its mirror image is the same as the number. All digits are the same. Guess my number. (Answer: 1111)
Guess My Number - Question 2: My number is a 4-digit number. The first and last digits are 8. The middle digits are 0. Its mirror image looks the same. Guess my number. (Answer: 8008)
Guess My Number - Question 3: My number is a 4-digit number. It uses only 0, 1 and 8. The middle two digits are 8. Guess my number. (Answer: 1881)
In simple words: Create number riddles using the digits 0, 1, and 8 that have mirror symmetry.

Exam Tip: When creating similar questions, give clear clues about the digits and their positions. This helps your friends narrow down the possibilities.

Question 21. What do you notice about the letters written on the ambulance? Why are they written this way? Discuss.
Answer: The word AMBULANCE is written in reverse (mirror image) on the front of the ambulance. It is written this way so that when drivers in front look at it through their rear-view mirror, the word appears correct and readable. This helps them quickly recognize the ambulance and give way without confusion. Writing the word in mirror image saves time and can help in emergencies, as people can immediately understand that an ambulance is coming.
In simple words: AMBULANCE is backwards on the ambulance. When drivers look in their rear-view mirror, it reads correctly and they know to move out of the way.

Exam Tip: Understanding real-world applications of symmetry (like the ambulance) shows that maths concepts are practical and useful in everyday life.

Question 22. Can you identify these words? Where will you place the mirror to read the following words correctly?
Answer: Place a vertical mirror on the right side to read the words correctly. PAT becomes TAP, HEN becomes NEH (or can be read as reversed HEN), WOW stays the same, and CAN becomes NAC (or appears as reversed CAN). For the given mirror words shown: PAT reads as TAP when reflected, HEN reads as NEH in mirror, WOW reads as WOW (it is the same), and CAN reads as NAC in mirror.
In simple words: Put a mirror on the right side of each backwards word. The mirror will show you what the word says correctly.

Exam Tip: When a word is written backwards, placing a mirror vertically on the right side will show the correct reading. Some words like WOW look the same forwards and backwards.

Question 23. Now, you try to write some words/names in this way and challenge your friends to guess them. Can you also try doing this with the script of your own language?
Answer: Place a vertical mirror on the right to read them correctly. Some examples: LOVE becomes EVOL (mirror: LOVE), MINE becomes ENIM (mirror: MINE), NICE becomes ECIN (mirror: NICE), ONE becomes ENO (mirror: ONE), LINE becomes ENIL (mirror: LINE). You can try the same activity with your own language script - write words backwards and ask friends to use a mirror to read them correctly.
In simple words: Write words backwards and have friends use a mirror to read them the right way.

Exam Tip: Creating your own mirror word challenges reinforces the concept of symmetry and reflection while making learning fun and interactive.

Question 24. Complete the following to make symmetrical shapes.
Answer: The shapes have been completed to be symmetrical. Each partial shape shown on the left has been mirrored and completed on the right. The completed designs show a vertical line of symmetry running down the middle, with both halves matching perfectly. The shapes include a pointed top shape, a V-shape at the bottom, and a horizontal line at the base - all reflected to create full symmetrical patterns.
In simple words: Draw the missing half of each shape so both sides match along the middle line.

Exam Tip: To complete symmetrical shapes, use the line of symmetry as your guide. Measure distances from the line on the given side, then mark matching distances on the blank side.

Question 25. Observe the shapes. How many sides does each shape have?
Answer: Looking at the three-sided shapes: triangles have 3 sides each. Looking at the four-sided shapes: rectangles have 4 sides, squares have 4 sides, a trapezoid (the orange shape in the second set) has 4 sides, a diamond shape has 4 sides, and a star shape has 10 sides (counting all the points). All triangles shown have 3 sides, and all quadrilaterals (four-sided shapes) have 4 sides.
In simple words: Count the straight lines that form the edge of each shape. Triangles have 3 sides, squares and rectangles have 4 sides.

Exam Tip: To count sides, trace around the shape's edge and count each straight section. Don't count corners, only the sides.

Question 26. How many lines of symmetry does each shape have? You may trace these shapes and check the lines of symmetry by folding the shapes.
Answer: From the three-sided shapes: most triangles have 0 lines of symmetry (irregular triangles), but an equilateral triangle has 3 lines of symmetry. From the four-sided shapes: the square has 4 lines of symmetry (two diagonal and two through the midpoints of opposite sides), the rectangle has 2 lines of symmetry (horizontal and vertical through the centre), the trapezoid has 0 lines of symmetry, the diamond or rhombus has 2 lines of symmetry (both diagonal), and the star shape has multiple lines of symmetry depending on its design (typically 2, 4, or more).
In simple words: Fold each shape different ways. Count how many fold lines make both halves match perfectly.

Exam Tip: Trace and cut out each shape, then fold it in different directions to find all lines of symmetry. A shape may have vertical, horizontal, or diagonal lines of symmetry.

Page 170

Tiling the Tiles

Here are some patterns with tiles. Find the repeating unit (tile) and keep going with the patterns.

Page 170 - Number of lines of Symmetry

The image shows two grids displaying various coloured shapes with dashed lines marking their symmetry lines. On the left side, there are shapes like triangles, pentagons, and diamonds in different colours (orange, blue, purple, and green). On the right side, there are more complex shapes including a purple diamond, blue rectangles, an orange trapezoid, a green triangle, a blue star, and an orange diamond shape. Each shape has dashed lines drawn through it to show where the shape can be folded so both halves match perfectly.

Page 171

Tiles at the Tile Shop

Bablu Chacha creates lovely tiles of the kinds shown below. Design your own creative tiles in the spaces given below. You may use a rangometry kit or shape cutouts.

Question 1. Which shapes have you used to make the tiles?
Answer: The tiles come from simple geometric shapes, chiefly Triangles (such as equilateral and right-angled triangles), Squares, Rhombuses (shapes that look like diamonds), and Hexagons. A lot of the brightly coloured tiles are built by putting the same triangles side by side in various ways.
In simple words: Tiles are made using triangles, squares, diamonds, and hexagons. Many colourful tiles come from putting the same triangles together in new arrangements.

Exam Tip: Look closely at each tile and spot the basic shapes inside it - name at least three different shapes you find.

Question 2. Which of the tiles are symmetrical? Draw the lines of symmetry (if any).
Answer: Several of the tiles display symmetry. The yellow and purple star tile has four lines of symmetry - two running through opposite points of the star, and two running through the midpoints between those points. The pink and white square tile has four lines of symmetry - two diagonal lines and two lines passing through the middle horizontally and vertically. These lines show where you can fold each tile so that both sides match up perfectly.

Exam Tip: Always fold or use a mirror to check if a shape is truly symmetrical - if one side mirrors the other exactly, the fold line is a line of symmetry.

Question 3. Make more tiles by joining two or more shapes.
Answer: You can combine triangles to form a larger hexagon, or arrange diamonds in a repeating pattern. You might also group squares together or blend triangles with diamonds to make fresh tiles. The key is ensuring that the shapes fit together with no gaps or overlaps, and that the resulting tile looks balanced and pleasing to the eye.
In simple words: Put shapes together in new ways. Make sure they fit perfectly with no spaces between them. Try triangles with diamonds, or squares in a line.

Exam Tip: When combining shapes, always check that edges match up perfectly - no gaps, no overlaps.

Question 4. Look at the following shapes. What do you notice?
Answer: We observe several things. Both designs are built by repeating a single shape many times. The shapes lock together without any empty spaces or parts overlapping. The way they are arranged stays the same, but the colour scheme changes. Due to this colour difference, the two designs appear unlike each other, even though their arrangement is identical. Both patterns show a repeating tile style, like what you see on a floor. We can understand that even when we work with the same shapes, shifting the colours or how they sit can lead to designs that look entirely new. Since I see that both designs use the same shapes put in the same way, with only the colours switched out, the shapes fill the surface with no spaces or overlaps, making a repeating pattern.
In simple words: Both designs use the same shapes arranged the same way. Changing the colours makes them look different, even though the pattern is the same.

Exam Tip: Notice that pattern and colour are two separate things - the same pattern can look completely different just by changing colours.

Symmetry in Patterns and Tile Designs in Class 4 Maths Mela

Page 172

Let Us Do

Question 1. Make floor patterns with your tile. Mini has made a floor pattern as shown below. Remember there should be no overlaps and no gaps.
Answer: A floor pattern has been created using a repeating tile made up of four coloured shapes - light green, salmon pink, bright yellow, and light blue rhombuses that fit together perfectly. This tile is repeated across the entire floor in rows, with each tile placed side by side and on top of the previous row. The colours shift in a consistent pattern, making the overall design eye-catching while keeping the arrangement neat and orderly. The shapes are placed so that they touch edge to edge with no gaps between them and no part of one tile overlapping another.
In simple words: The floor is covered with a repeating tile made of four coloured diamonds. Each diamond shape touches the others with no spaces or overlap between them.

Exam Tip: For floor patterns, always ensure shapes fit perfectly with no gaps - this shows you understand how tiling works.

Question 2. Making a catty wall! Create more of these tiles. Some ideas to make creative wall patterns are given below.
Answer: A creative wall pattern has been built using a repeating tile made of four small right triangles, each in a different colour - blue, orange, pink, and lime green. When four of these triangles come together, they form a square tile. This square tile is then repeated many times across the wall in a checkerboard style, with each square touching the next. The colours of each triangle within the tile shift around, creating a spinning or pinwheel look that makes the wall eye-catching and lively. The tiles fit perfectly without any gaps or overlaps, and the colour scheme - including blues, oranges, pinks, and bright greens - gives the wall a cheerful, modern feel.
In simple words: Four coloured triangles join to make one square tile. These tiles repeat to cover the whole wall. The colours make a pretty pinwheel pattern.

Exam Tip: When making wall patterns, think about how colours and shapes can rotate or shift to create movement and visual interest.

Question 3. Let us go on a nature walk (Project time). Go for a nature walk to a nearby park or around your school with your teacher or your parents. Observe the patterns, designs, or symmetry around you carefully. Collect leaves, petals, and flowers that have fallen on the ground. In your project file: - Categorise the leaves into symmetrical and non-symmetrical. - Make different designs and patterns with leaves and flowers. - Make a greeting card using imprints of leaves or dry flowers. - Create animals or designs using leaves and flowers.
Answer: I took a nature walk to a nearby park with my parents. I watched the leaves, flowers, and butterflies around me with care. I saw that a lot of leaves and butterflies have symmetry - both sides appear the same when we fold them down the middle. In my project file, I did these things: I gathered leaves and sorted them into those with symmetry and those without. I made several new designs and patterns by putting leaves and flowers in different orders. I created a greeting card using stamps made from leaves or dried flowers that I pressed onto paper. I also used leaves and flowers to build animals and other designs. Doing this activity was engaging and taught me how symmetry appears in the world around us.
In simple words: I went to a park and found leaves and flowers. Many leaves have two sides that match - that is symmetry. I sorted them, made patterns, and created a greeting card.

Exam Tip: When observing nature, fold items down the middle to check if both halves are identical - this is the simplest way to spot symmetry.