CLASS 4 MATHS WORKSHEET LESSON 11

Fun with Symmetry (Preparatory Stage Math)

Concepts • Computational Skills • Problem-Solving & Modeling • 10 questions each • 40% Easy, 40% Average, 20% Challenging • One toggle shows Answer + Solution

Worksheet A: Concepts

Easy

Q1. An ink-blot made by folding a paper looks the same on both sides of a central line. What is this line called?

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Answer

Line of symmetry.

Solution

In the ink design activity, the fold that divides the figure into two equal mirror halves is the line of symmetry.

Easy

Q2. A paper airplane with a neat center fold flies straighter. What does that center fold represent in symmetry terms?

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Answer

A symmetry line.

Solution

The central crease makes left and right halves match; it is a mirror line for the model.

Easy

Q3. Circle the symmetric figure idea: butterfly wings, random scribble, leaf with midrib (choose the clearly symmetric ones).

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Answer

Butterfly wings; many leaves with a midrib.

Solution

Natural examples often show bilateral symmetry, where one side mirrors the other across a line.

Easy

Q4. Which has more lines of symmetry typically: a rectangle or a regular hexagon?

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Answer

Regular hexagon.

Solution

A rectangle has 2 lines of symmetry; a regular hexagon has 6, one through each vertex and opposite side midpoint.

Average

Q5. A square is folded along a diagonal. Do the halves match exactly? What is this fold called in symmetry language?

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Answer

Yes; a line of symmetry (diagonal).

Solution

Squares have 4 symmetry lines: two medians and two diagonals that map the shape onto itself.

Average

Q6. Which digits look the same in a vertical mirror placed at the center line: 0, 1, 2, 3, 8 (choose all that work with a vertical mirror)?

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Answer

0, 1, 8 (common fonts).

Solution

These digits often have vertical mirror symmetry; 2 and 3 typically do not in standard print.

Average

Q7. A regular triangle (equilateral) is traced. How many lines of symmetry can be drawn on it?

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Answer

Three.

Solution

Each vertex to the midpoint of the opposite side is a symmetry line for an equilateral triangle.

Average

Q8. A rectangle is folded along its longer midline. What transformation maps one half onto the other across that line: reflection, rotation, or translation?

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Answer

Reflection.

Solution

A symmetry line produces a mirror reflection; the halves match when folded across the line.

Challenging

Q9. A regular pentagon has 5 lines of symmetry. Describe in words where each symmetry line passes (no drawing needed).

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Answer

From each vertex through the midpoint of the opposite side.

Solution

Equal edge lengths and angles ensure each vertex–opposite-side-midpoint line splits the polygon into mirror halves.

Challenging

Q10. A tiling pattern repeats by sliding a single tile without gaps/overlaps. Name the transformation and explain why the pattern still fits perfectly.

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Answer

Translation (sliding).

Solution

Sliding preserves size and shape, so copies align edge-to-edge, keeping a gapless tessellation.

Worksheet B: Computational Skills

Easy

Q1. Count lines of symmetry: square, rectangle (write as “square — __; rectangle — __”).

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Answer

Square — 4; Rectangle — 2.

Solution

Square: two medians and two diagonals; rectangle: two medians only (for a non-square rectangle).

Easy

Q2. Choose the mirror that works: to mirror the right half of a heart to make a full heart, place the mirror on the left or at the bottom?

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Answer

On the left (vertical mirror line).

Solution

Hearts are usually symmetrical across a vertical line, matching left and right halves.

Easy

Q3. Tick the letters likely symmetric in a vertical mirror (block capitals): A, H, M, N, O, T, X, Y (choose the common ones that work in standard fonts).

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Answer

A, H, M, O, T, X, Y (font-dependent).

Solution

These often have vertical symmetry; N typically does not in its usual slanted form.

Easy

Q4. A regular hexagon: write the number of sides and number of symmetry lines as a pair (__, __).

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Answer

(6, 6).

Solution

Regular polygons have as many symmetry lines as sides; each line splits the figure into equal mirrored halves.

Average

Q5. Complete the half: a shape’s left half is drawn; describe which mirror line (vertical/horizontal) is needed to complete it to a symmetric whole (no drawing required; choose one and justify briefly).

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Answer

Vertical mirror (typical for left-half drawings).

Solution

Completing a left half needs a vertical line so right half mirrors across that line.

Average

Q6. A star tile is copied by flipping across a line. Name the transformation and state if the copy is congruent to the original (yes/no).

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Answer

Reflection (flip); yes, congruent.

Solution

Reflections preserve size/shape; the image matches exactly though orientation reverses.

Average

Q7. A border pattern repeats by turning each tile 90°. Name the transformation and whether gaps/overlaps appear if the tile is a square (yes/no).

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Answer

Rotation; no gaps/overlaps for square tiles.

Solution

Rotating a square by 90° keeps edges aligned in a tessellation.

Average

Q8. In a 2×2 block of an addition table, compare the sum of the main diagonal with the other diagonal. Same or different, and why (one sentence)?

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Answer

Same.

Solution

Both diagonals sum to equal totals because entries increase by the same step across rows/columns.

Challenging

Q9. A shape has exactly two lines of symmetry: one vertical and one horizontal. Name two common shapes that fit (non-rotated), and explain in a phrase why they have 2 lines (not 4).

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Answer

Rectangle, plus-sign with equal arms.

Solution

They match across vertical and horizontal axes; diagonals don’t map halves unless it’s a square or special cross.

Challenging

Q10. A pattern uses sliding and flipping the same tile to cover a floor with no gaps. Which set of transformations is used together, and what property must the tile have to tessellate well?

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Answer

Translations and reflections; edges meeting without gaps (edge-to-edge tiling).

Solution

Copies must fit perfectly—tile shapes with compatible angles/edges tessellate under slides and flips.

Worksheet C: Problem-Solving & Modeling

Easy

Q1. Mirror digits challenge: Make a 3-digit number near 120 that looks the same in a vertical mirror. Write one example and state where the mirror is placed (left/right middle line).

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Answer

101 (mirror at center line).

Solution

Digits like 1 and 0 keep their look in vertical mirrors; choose such digits to build numbers with mirror symmetry.

Easy

Q2. “AMBULANCE” is written reversed on the vehicle’s front. Why is it written that way in terms of mirror reading in a rear-view mirror?

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Answer

So drivers see it correct in their mirrors.

Solution

Rear-view mirrors reverse left-right, so reversed lettering appears normal to drivers ahead.

Easy

Q3. Leaf collection: Sort three leaves into “symmetric” and “not symmetric” piles by imagining a fold line. How many go to each pile if two are fold-symmetric and one is not?

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Answer

Two symmetric; one not.

Solution

Use a pretend fold to test if halves match; this operationalizes the definition of symmetry.

Easy

Q4. Paper cut-and-open: Fold once and cut a small triangle on the fold edge. After opening, how many triangles appear and why do they look mirrored?

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Answer

Two mirrored triangles.

Solution

Cut on the fold duplicates across the mirror line, producing a reflected pair after unfolding.

Average

Q5. Tiling: A floor uses only rectangles. Which moves can generate the pattern from one rectangle—slide, flip, rotate—and will they still tile without gaps? Explain briefly.

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Answer

Slide/rotate/flip; yes, still no gaps.

Solution

Rectangles tessellate under all rigid motions since right angles and equal opposite sides align perfectly.

Average

Q6. Complete a half-rangoli: With a vertical mirror, describe how to place dots or strokes on the other side to keep symmetry intact (2–3 steps in words).

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Answer

Reflect points across the line at equal distances.

Solution

For each dot/curve on the left, plot a matching point the same distance on the right, then copy the curve shape mirrored.

Average

Q7. Mirror-words: Choose which will read the same in a vertical mirror (block style): WOW, MOM, CAT, OHO. Pick and justify briefly.

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Answer

WOW, MOM, OHO (font-dependent).

Solution

These consist of letters with vertical symmetry; CAT changes in a mirror and won’t read the same.

Average

Q8. Symmetry count in polygons: Name a polygon with exactly 1 line of symmetry and one with 0, using familiar classroom cutouts (name both shapes).

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Answer

Isosceles triangle (1); scalene triangle (0).

Solution

Equal legs in isosceles give one mirror; no equal sides/angles in scalene yields none.

Challenging

Q9. Holes-and-cuts: Fold a square twice (into quarters) and cut a small square at the folded corner. After opening fully, how many small squares appear and where are they located (center/corners/edges)?

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Answer

Four small squares at the four corners.

Solution

The cut at the multilayer corner replicates to all four corners after unfolding due to symmetry in both folds.

Challenging

Q10. Mirror numbers: Create a 4-digit number whose mirror image is the same with a vertical mirror. Explain the letter/digit property that allows this (give one example).

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Answer

1001; uses digits with vertical symmetry and palindromic placement.

Solution

Choose digits like 1 and 0 that are vertically symmetric and arrange as a palindrome to keep the mirror identical.

Teacher Notes

Activities reflect Chapter 11’s ink-blot, folding, mirror placement, mirror-digit tasks, symmetry counts in regular polygons, and tiling via slide/flip/rotate. Each “Show solution” reveals both the answer and a child-friendly explanation to support self-checking, observation, and mathematical communication in line with NCERT’s experiential approach.