NCERT Solutions for Class 5th Maths Chapter 10 The green-and-pink square, and colouring a square for a 1/4 turn — Let Us Think
Book page 139 Updated on2026-09-19
Q1.
Does this design look the same after 1/2 turn? __________The design: four small squares — two green and two pink — placed corner to corner.
Answer
Yes. The design looks exactly the same after a 1/2 turn.
The design is a big square cut into four small squares. Green sits at the top-left and at the bottom-right. Pink sits at the top-right and at the bottom-left.
A half turn swaps opposite corners, and opposite corners have the same colour.
Top-left (green) goes to bottom-right, which is green ✓ Top-right (pink) goes to bottom-left, which is pink ✓ Bottom-left (pink) goes to top-right, which is pink ✓ Bottom-right (green) goes to top-left, which is green ✓ So the design looks the same after a 1/2 turn
Why it happens: A half turn always sends a corner square to the square diagonally opposite. Here the diagonal pairs are green–green and pink–pink. Same colour meets same colour, so nothing appears to change.
Q2.
Does the design look the same after 1/4 turn? __________The design: four small squares — two green and two pink — placed corner to corner.
Answer
No. After a 1/4 turn the colours swap places, so the design looks different.
Green has moved to where pink was, so this is not the same picture.
A 1/4 turn sends the top-left square to the top-right place. Top-left is green. Top-right was pink. Green now sits where pink used to be → the design has changed
Why: A quarter turn sends each square to the square next to it, not the one opposite. Neighbouring squares here have different colours, so the change shows at once.
Remember: A design can look the same after a 1/2 turn but not after a 1/4 turn. The 1/2 turn is the easier test to pass.
Q3.
Colour the square given in the adjoining figure using two colours so that the design looks the same after every 1/4 turn.The square printed in the book. The dashed lines — both diagonals and both middle lines — divide it into eight equal triangles round the centre.
Answer
Colour the eight triangles turn by turn — orange, blue, orange, blue — all the way round. That is the only way to do it with two colours.
The square in the book is already divided by dashed lines: both diagonals and both middle lines. That makes 8 equal triangles round the centre.
Eight triangles, coloured alternately. This makes a pinwheel pattern.
How to colour it, step by step:
Count the triangles. The dashed lines make 8 equal triangles round the centre.
Start anywhere and colour that triangle orange.
Colour the next one round blue.
Keep going round — orange, blue, orange, blue — until all 8 are coloured.
You will have 4 orange triangles and 4 blue triangles, sitting in a pinwheel pattern.
Why this works: A 1/4 turn moves each triangle two places round the ring. Counting round the ring, place 1 goes to place 3, place 2 to place 4, and so on. If you colour turn by turn, place 1 and place 3 are the same colour, place 2 and place 4 are the same colour — so every triangle lands on its own colour.
Check it yourself: Trace your coloured square on tracing paper. Put a pin at the centre and turn the tracing a quarter of the way round. The colours should sit exactly on top of the ones below.
Q4.
How many times does this shape look the same during a full turn?The square printed in the book. The dashed lines — both diagonals and both middle lines — divide it into eight equal triangles round the centre.
Answer
4 times — at the 1/4 turn, the 1/2 turn, the 3/4 turn and the full turn.
Full turn = 1 It looks the same after every 1/4 turn How many quarter turns in a full turn? 1 ÷ 1/4 = 4 So it looks the same 4 times in one full turn
The same picture appears four times while the square goes once round.
Why it is 4 and not 8: There are 8 triangles, but they are of two colours. A shift of one triangle would put orange on blue. Only a shift of two triangles — that is a quarter turn — keeps the colours right. Four such shifts make one full turn.
Tip for any design: Count how many equal, identical parts go round the centre. That number is how many times the design looks the same in one full turn.
Q5.
Do these designs have reflection symmetry also? Draw the line(s) of symmetry.The design: four small squares — two green and two pink — placed corner to corner.The square printed in the book. The dashed lines — both diagonals and both middle lines — divide it into eight equal triangles round the centre.
Answer
The green-and-pink square: yes — it has 2 lines of symmetry, both slanting (the two diagonals). The pinwheel square you coloured: no — it has no line of symmetry at all.
The pinwheel turns beautifully but never folds onto itself.
The green-and-pink square — test each fold:
Fold side to side. Green (top-left) lands on pink (top-right). ✗
Fold top to bottom. Green lands on pink again. ✗
Fold along the slanting line from top-left to bottom-right. Green stays on green, and the two pink squares swap. ✓
Fold along the other slanting line. Pink stays on pink, and the two green squares swap. ✓
So it has 2 lines of symmetry — the two diagonals.
The pinwheel square — test each fold:
Fold side to side, top to bottom, or along either diagonal.
Every time, an orange triangle lands on a blue triangle. ✗
So the pinwheel has no line of symmetry.
Why the pinwheel cannot fold: The colours go round in one direction — orange, blue, orange, blue. A fold reverses the direction, so the order becomes blue, orange, blue, orange. That is the opposite of what is printed, and it never matches.
Big idea: The pinwheel has rotational symmetry but no reflection symmetry. The letter V has reflection symmetry but no rotational symmetry. The letter X and design (c) have both. All four kinds are possible.