Mathematics Worksheet: Symmetry & Patterns (Preparatory Stage)
Based on NCERT/CBSE "Symmetrical Designs". Explore reflection, rotational symmetry, patterns, and real-world design. Click "Show Answer" and then "Show Solution" for each.
Concepts (Symmetry & Patterns)
- Name two letters with a vertical line of symmetry.
Show Answer
Answer: A, MShow Solution
Solution: Draw a vertical line down the middle—both sides match (from the book's alphabet exercise). - Which alphabets have a horizontal line of symmetry?
Show Answer
Answer: B, C, D, E, H, I, K, O, XShow Solution
Solution: If folded along the center horizontal line, top matches bottom. - What is reflection symmetry?
Show Answer
Answer: When one half is a mirror image of the other.Show Solution
Solution: Like folding along a line and both halves overlap exactly. - How many lines of symmetry does the letter H have?
Show Answer
Answer: 2Show Solution
Solution: Vertical and horizontal lines each split H into mirror halves. - Give an example of a real object with reflection symmetry.
Show Answer
Answer: Butterfly, leaf, heartShow Solution
Solution: When folded through the centerline, both parts match. - Which digit(s) have both vertical and horizontal symmetry?
Show Answer
Answer: 0, 8Show Solution
Solution: Fold horizontally or vertically—halves match for 0 and 8. - Explain rotational symmetry with an example.
Show Answer
Answer: A firki (paper pinwheel) or letter HShow Solution
Solution: Rotating these shapes partway (< 360°) and they look the same. - If you fold paper along a line and both halves overlap, what is this line called?
Show Answer
Answer: Line of symmetryShow Solution
Solution: This line splits the figure into two mirror-image parts. - What is the minimum number of cuts to make an H by folding?
Show Answer
Answer: Two (for 1/4th, then cut, per book's folding activity)Show Solution
Solution: Fold horizontally and vertically, cut shape along outline. - Which shape remains unchanged on 1/2 turn rotation?
Show Answer
Answer: Square, H, XShow Solution
Solution: After 180° (half-turn), shape/letter looks the same.
Computational Skills (Visualization & Construction)
- If a square is colored half red and half blue along a line of symmetry, how many lines could you use?
Show Answer
Answer: 4Show Solution
Solution: Horizontal, vertical, and both diagonals; all divide it exactly in half. - If you join two triangles by one side, what new shape can be formed?
Show Answer
Answer: Parallelogram or rhombusShow Solution
Solution: Common textbook tangram task: two equal triangles form a parallelogram or rhombus. - What letter has only one vertical line of symmetry?
Show Answer
Answer: A or MShow Solution
Solution: Only a vertical fold makes mirror halves. - If you make a windmill (firki) by folding a square diagonally, how many axes does it have?
Show Answer
Answer: 2 diagonal axesShow Solution
Solution: Book’s “Make a Windmill” steps show folds along two diagonals. - If a rectangle measures 8 cm by 4 cm, draw all lines of symmetry.
Show Answer
Answer: 2 lines (vertical and horizontal through center)Show Solution
Solution: Rectangles have only 2 such lines. - You draw a circle and mark its diameter. How many lines of symmetry does a circle have?
Show Answer
Answer: InfiniteShow Solution
Solution: Any diameter across the circle is a line of symmetry. - If a block print design is rotated 1/4 turn 4 times, what order of symmetry does it show?
Show Answer
Answer: 4-fold (or order 4) rotational symmetryShow Solution
Solution: It repeats every 90°, so four times fills the circle. - In the number 1001, how many lines of symmetry does it have (if any)?
Show Answer
Answer: 1 (vertical)Show Solution
Solution: 1001 is a reflection palindrome; vertical line through center. - If a design remains unchanged after a 1/3 turn, how many times in one rotation does it look the same?
Show Answer
Answer: 3 timesShow Solution
Solution: After every 120° turn, it repeats. - How many lines of symmetry do each of these have: (a) hexagon (b) equilateral triangle?
Show Answer
Answer: (a) 6 lines; (b) 3 linesShow Solution
Solution: Regular hexagon has 6; triangle has 3 (one through each vertex and opposite side).
Problem-Solving & Real-World Modeling
- Lali decorates a card so it's the same if turned upside down. What kind of symmetry?
Show Answer
Answer: Rotational symmetry (order 2)Show Solution
Solution: “Same when upside down” means unchanged at half a turn (180°). - Use a mirror: which letters will look unchanged in a vertical mirror? (List 3)
Show Answer
Answer: A, M, TShow Solution
Solution: Mirrors create reflection symmetry—check what matches with the mirror’s edge. - Give an example of a two-digit number with both reflection and rotation symmetry.
Show Answer
Answer: 88Show Solution
Solution: 88 remains same when flipped or reflected. - Block-print artisans make a symmetrical pattern, but one block is rotated wrongly. Will the symmetry remain?
Show Answer
Answer: NoShow Solution
Solution: Symmetry is broken if repeats are not rotated consistently. - If you create a rangoli that looks exactly the same after a 1/2 turn and has 2 lines of symmetry, what shapes could you use?
Show Answer
Answer: Squares, rectangles, certain crossesShow Solution
Solution: Shapes with order 2 rotation and 2 symmetry axes. - Design a border for a card where the pattern repeats every 1/4 turn. How many times will the pattern appear around a square card?
Show Answer
Answer: 4 timesShow Solution
Solution: 360°/90° = 4 times. - How can you use both mirror and fold symmetry to make a diya design?
Show Answer
Answer: Fold paper for outline, then decorate both halves identicallyShow Solution
Solution: Like NCERT’s cut-out: fold along the line of symmetry, cut/decorate equally. - After rotating a block print by 1/4 turn, the design looks unchanged. If rotated 1/2 turn, unchanged. Is this also mirror-symmetric?
Show Answer
Answer: Possibly, but not alwaysShow Solution
Solution: Some designs with rotation also allow reflection, but not all—need to check if left/right halves match. - What geometric tool helps you check reflection symmetry of a drawing?
Show Answer
Answer: MirrorShow Solution
Solution: Place the mirror on line; see if other half matches. - If you make a design from 6 triangles meeting at a point, what symmetry does it have?
Show Answer
Answer: 6-fold rotational symmetryShow Solution
Solution: Each triangle’s 1/6 turn repeats 6 times in one full rotation.