Question Letter E
Can E be cut by drawing only half?
Steps only
Fold horizontally through the middle; the top and bottom arms match.
Answer
Yes, using its horizontal line of symmetry.
CLASS 5 · MATHS MELA · CHAPTER 10
Symmetrical Designs
Recognise reflection and rotational symmetry in letters, digits, geometric arrangements and repeated block-print patterns.
49 worked answersAll 4 exercise sets
What you will learn
- Identify and draw lines of reflection symmetry.
- Find the smallest turn that maps a design onto itself.
- Create original patterns with stated symmetry rules.
49 worked answers · short steps first, explanations when you need them
Alphabet Cutouts and Reflection Symmetry
Textbook pages 136
Question Letter N
Can N be made from a half or quarter reflection cutout?
Steps only
A vertical or horizontal reflection reverses the diagonal.
Answer
No, not by the shown vertical or horizontal fold.
Question Letter X
Can X be cut from a half or quarter?
Steps only
X has both vertical and horizontal reflection lines.
Answer
Yes; a quarter is enough.
Question Letter T
Can T be cut from a half?
Steps only
Fold vertically through the stem.
Answer
Yes, using its vertical line of symmetry.
Question Letter K
Can K be cut from a half?
Steps only
Fold horizontally through the midpoint; the two diagonal arms exchange.
Answer
Yes, using its horizontal line of symmetry.
Question Letter V
Can V be cut from a half?
Steps only
Fold vertically through the point and middle of the opening.
Answer
Yes, using its vertical line of symmetry.
Question Letter O
Can O be cut from a quarter?
Steps only
Fold once vertically and once horizontally.
Answer
Yes; a quarter is enough.
Question Horizontal letters
Among E, N, X, T, K, V and O, which have a horizontal line of symmetry?
Steps only
Reflect each across a line through its middle.
Answer
E, X, K and O.
Question Vertical letters
Which listed letters have a vertical line of symmetry?
Steps only
Compare left and right halves.
Answer
X, T, V and O.
Question Both letters
Which listed letters have both horizontal and vertical symmetry?
Steps only
Take the intersection of the two lists.
Answer
X and O.
Question Paper designs
How can a symmetric diya or boat cutout be made?
Steps only
Choose a reflection line, fold along it and draw only one side touching the fold.
Cut the outline without separating the fold, then open.
Answer
Any design whose unfolded halves mirror exactly is valid.
Windmill, Letters and Digit Rotations
Textbook pages 137–138
Question Firki quarter
Does the four-bladed firki look the same after a quarter turn?
Steps only
A quarter turn moves every blade to the next identical blade.
Answer
Yes.
Question Firki half
Does it match after a half turn?
Steps only
Two quarter turns also map blades onto identical blades.
Answer
Yes.
Question Firki three-quarter
Does it match after a three-quarter turn?
Steps only
Three identical blade positions are advanced.
Answer
Yes.
Question Firki full
Does it match after a full turn?
Steps only
Every object returns after 360°.
Answer
Yes.
Question Letter H
At which non-full turn does H match?
Steps only
Rotate its marked corners through 180°.
Answer
At 1/2 turn.
Question Letter I
At which non-full turn does the displayed I match?
Steps only
The rounded vertical bar has matching ends.
Answer
At 1/2 turn.
Question Letter X
At which turns does X match?
Steps only
Its four arms are identical and equally spaced.
Answer
At 1/4, 1/2 and 3/4 turns.
Question Letter Y
Does Y have non-trivial rotational symmetry?
Steps only
After a half turn, its single stem points upward and does not coincide.
Answer
No; it matches only after a full turn.
Question Digit reflection
Which displayed digits have reflection symmetry?
Steps only
Check vertical and horizontal mirror lines in the printed font.
Answer
0, 1, 3 and 8.
Question Digit rotation
Which displayed digits have rotational symmetry?
Steps only
Turn each digit through 180°.
Answer
0, 1 and 8.
Question Digit both
Which digits have both reflection and rotational symmetry?
Steps only
Intersect the two lists.
Answer
0, 1 and 8.
Question 11
Does 11 have reflection or rotational symmetry in this font?
Steps only
The two identical simple 1s exchange under vertical reflection and half turn; each 1 also matches horizontally.
Answer
Both reflection and half-turn rotational symmetry.
Question 1001
Does 1001 have reflection or rotational symmetry?
Steps only
It is a palindrome and 0 and 1 each survive a half turn in the shown font.
Answer
Both reflection and half-turn rotational symmetry.
Question Number examples
Give 2-, 3- and 4-digit examples with both symmetries.
Steps only
Use palindromes made only from 0, 1 and 8.
Answer
Examples: 88, 808 and 8008.
Making and Colouring Symmetric Designs
Textbook pages 139
Question (a)
Does the starting cross design with one extra circle on the right have rotational symmetry?
Steps only
After a half or quarter turn, the extra circle moves to an empty location.
Answer
No.
Question (b)
How can the design be changed to match after a half turn?
Steps only
Add an identical outer circle the same distance to the left of the centre.
Answer
Add a matching circle opposite the existing right-hand circle.
Question (c)
How can it be changed to match after a quarter turn?
Steps only
Keep the right outer circle and add identical outer circles above, left and below at the same radius.
Answer
Use four identical outer circles, one in each main direction.
Question (d)
Do the completed designs also have reflection symmetry?
Steps only
The half-turn version reflects across horizontal and vertical axes when the opposite circles align.
The four-circle version also reflects across both diagonals.
Answer
Yes; the balanced construction has horizontal and vertical lines, and the quarter-turn version can have four reflection lines.
Question Checker half
Does the 2×2 diagonal-colour checker match after a half turn?
Steps only
Each green square maps to the other green square and each red to the other red.
Answer
Yes.
Question Checker quarter
Does the checker match after a quarter turn?
Steps only
A green square moves to a red position.
Answer
No.
Question Eight sectors
Colour eight triangular sectors using two colours so the square matches every quarter turn.
Steps only
Colour the sectors alternately A,B,A,B around the centre.
A quarter turn advances two sectors, so each colour maps to itself.
Answer
Use alternating colours around the eight sectors.
Question Matching count
How many times does a quarter-turn-symmetric shape match during one full turn?
Steps only
Matches occur at 1/4, 1/2, 3/4 and 1 full turn.
Answer
4 times.
Question Sector reflections
Does the alternating eight-sector design have reflection symmetry?
Steps only
Test axes through opposite sector centres and opposite boundaries.
Answer
Yes; it can have 4 reflection lines through the centre.
Question Shape construction
Make symmetric designs from equal-sided squares and equilateral triangles.
Steps only
Place pieces in equal pairs on opposite sides of a chosen axis, or repeat one cluster every quarter turn.
Answer
Any non-overlapping arrangement satisfying the chosen reflection or rotation rule is valid.
Shape Classification and Block Prints
Textbook pages 140–141
Question Composite reflection
Does the displayed two-row square-and-triangle strip have reflection symmetry?
Steps only
A vertical reflection exchanges the left and right triangle pairs.
A horizontal reflection exchanges the two identical rows.
Answer
Yes; it has horizontal and vertical lines of symmetry.
Question Composite rotation
Does the strip have rotational symmetry?
Steps only
A half turn exchanges top-left with bottom-right and preserves every piece.
A quarter turn changes the long horizontal outline to vertical.
Answer
Yes, at 1/2 turn only.
Question Composite both
Does the strip have both types of symmetry?
Steps only
It passes both the reflection and half-turn tests.
Answer
Yes.
Question Sort designs
How should student-made designs be sorted?
Steps only
Test reflections first, then turns smaller than a full turn.
Answer
Place each into: only reflection, only rotation, both, or neither if it fails both tests.
Question Block (i)
Match wooden block (i) to its partial print.
Steps only
Compare the outline, internal veins or petals and the straight cut edge.
Answer
print (c).
Question Block (ii)
Match wooden block (ii) to its partial print.
Steps only
Compare the outline, internal veins or petals and the straight cut edge.
Answer
print (d).
Question Block (iii)
Match wooden block (iii) to its partial print.
Steps only
Compare the outline, internal veins or petals and the straight cut edge.
Answer
print (a).
Question Block (iv)
Match wooden block (iv) to its partial print.
Steps only
Compare the outline, internal veins or petals and the straight cut edge.
Answer
print (e).
Question Block (v)
Match wooden block (v) to its partial print.
Steps only
Compare the outline, internal veins or petals and the straight cut edge.
Answer
print (b).
Question Design A
At what turns does four-copy design A match?
Steps only
Four identical leaf prints point up, right, down and left.
Answer
Every 1/4 turn.
Question Design B turn
At what turn does four-heart design B match?
Steps only
The four equal heart motifs are arranged around one centre.
Answer
Every 1/4 turn.
Question Design B reflection
What other symmetry does design B have?
Steps only
The dashed vertical and horizontal axes split matching halves.
Answer
Reflection symmetry as well as rotational symmetry.
Question Border shapes
How should the border shapes be marked for symmetry?
Steps only
Give ✓ if at least one mirror line maps the complete coloured shape to itself.
Give * if a turn smaller than one full turn maps colours and outline to themselves.
Answer
Regular uncoloured shapes usually receive both marks; asymmetric or unevenly coloured shapes may receive neither or only one.
Question Vegetable blocks
Create an original symmetrical vegetable-block pattern.
Steps only
Choose one clear print as a repeat unit.
For reflection, stamp mirrored pairs across a guideline; for rotation, stamp equal copies at equal angles around a centre.
Answer
Any clean pattern with a stated and verifiable symmetry rule is valid.