NCERT Solutions Ganita Prakash Chapter 9 & 240Playing with Tiles — Playing with Tiles
Book page 239 Updated on2026-09-05
Q1.
Use the colour tiles given at the end of the book to complete the following figure so that it has exactly 2 lines of symmetry.
Answer
Each tile is a small square cut along a diagonal — one half yellow, one half blue. The figure in the book is an 8 × 8 grid with only the top-left 4 × 4 corner filled, and the two red lines drawn through the middle show where the lines of symmetry are to be.
How to complete it:
Mirror the given 4 × 4 block across the vertical red line. Place the tiles in the top-right block so that each one is the mirror image of the tile facing it — the yellow and blue triangles must swap sides.
Now mirror the whole top half across the horizontal red line to fill the bottom half in the same way.
The finished 8 × 8 design then has exactly 2 lines of symmetry — the vertical red line and the horizontal red line.
Careful with the tiles: a mirror does not simply slide a tile across — it flips it. If a tile's colour boundary runs from the bottom-left corner to the top-right corner, its mirror image in a vertical line runs from the bottom-right to the top-left.
Q2.
Use 16 such tiles to make figures that have exactly: 1 line of symmetry; 2 lines of symmetry.
Answer
Sixteen tiles fit neatly into a 4 × 4 square. Work like this:
Exactly 1 line of symmetry
Fix one line — say the vertical line down the middle of the 4 × 4 square.
Arrange the 8 tiles of the left half in any pattern you like.
Fill the right half with the mirror images of those tiles.
Make sure the pattern is not also symmetric top-to-bottom — for instance, use more blue at the top than at the bottom. Then the only line of symmetry is the vertical one.
Exactly 2 lines of symmetry
Arrange only the 4 tiles of the top-left quarter.
Mirror that quarter across the vertical middle line, then mirror the whole top half across the horizontal middle line.
Keep the quarter itself not symmetric about its own diagonal, otherwise you would get 4 lines of symmetry instead of 2.
Check it yourself: hold a small mirror upright along the line you claim, and see whether the half plus its reflection matches your design exactly. Then try the other three possible lines — they must fail.
Q3.
Use these tiles in making creative symmetric designs.
Answer
This is an activity — here are some designs worth trying with the two-coloured tiles:
A rangoli square: design one quarter and repeat it round the centre. Turning it by 90° gives a design with 4 lines of symmetry and order 4.
A pinwheel: place four identical quarters, each turned by 90° (not mirrored). This has rotational symmetry of order 4 but no line of symmetry — just like the paper windmill on page 230.
A border strip for a chart or a greeting card: repeat one small motif again and again along a line, with a mirror at every join.
A chessboard-style design: alternate the tiles so that the blue triangles form big diamonds.
The one rule behind all of them: decide first how the design should repeat — by folding (mirror) or by turning (rotation) — then build only one piece carefully and copy it that way.