NCERT Solutions for Class 5th Maths Chapter 10 Four blue squares with a triangle on each side — Symmetry in a Shape
Book page 140 Updated on2026-09-19
Q1.
Does this shape have reflection symmetry? If yes, draw its line(s) of symmetry.The shape: four blue squares joined in a block, with a cream triangle on the outer edge of each square on the left and on the right.
Answer
Yes. This shape has 2 lines of symmetry — one upright and one flat, both passing through the middle.
First see what the shape is made of: four blue squares joined in a block, with a cream triangle on the outer edge of each square on the left and on the right.
Fold along either red line and the two halves cover each other exactly.
Test each fold:
Fold along the upright line (between the left squares and the right squares). The two left triangles land on the two right triangles. The two left squares land on the two right squares. ✓
Fold along the flat line (between the top squares and the bottom squares). The upper triangle on each side lands on the lower triangle on that side. ✓
Try a slanting fold. A triangle would have to land on the top edge of the block, where there is no triangle. ✗
Upright fold → works ✓ Flat fold → works ✓ Slanting folds → do not work ✗ Number of lines of symmetry = 2
Why the slanting fold fails: There are triangles on the left and the right, but none on the top or the bottom. A slanting fold tries to send a left triangle up to the top, and there is nothing there to match it.
Q2.
Does it have rotational symmetry? If yes, at which turn?The shape: four blue squares joined in a block, with a cream triangle on the outer edge of each square on the left and on the right.
Answer
Yes — at a 1/2 turn. It does not look the same after a 1/4 turn.
The left pair of triangles swaps with the right pair, and the block of squares stays a block.
1/4 turn → the side triangles would move to the top and bottom → does not match 1/2 turn → left triangles go to the right, right triangles go to the left → matches ✓ 3/4 turn → does not match So: rotational symmetry at a 1/2 turn, and the shape looks the same 2 times in a full turn
Why: The shape is built the same way on the left and on the right. A half turn simply swaps those two sides, and since they are alike, nothing looks different. A quarter turn would move them to the top and bottom, where the shape is plain.
Q3.
Does it have both symmetries?The shape: four blue squares joined in a block, with a cream triangle on the outer edge of each square on the left and on the right.
Answer
Yes. This shape has both reflection symmetry and rotational symmetry.
Kind of symmetry
Does the shape have it?
Details
Reflection symmetry
Yes
2 lines — one upright, one flat
Rotational symmetry
Yes
at a 1/2 turn; looks the same 2 times in a full turn
Why the two go together here: Folding along the upright line and then along the flat line has the same effect as turning the shape half way round. So once a shape has two lines of symmetry crossing at right angles, it must also look the same after a half turn.
Check it yourself: Trace the shape. Fold your tracing side to side, open it, then fold it top to bottom. Now instead, turn the tracing half way round. You end up with the same picture both ways.
Q4.
Now, make your designs. Sort your designs in 3 categories — designs with only rotational symmetry, designs with only reflection symmetry, and designs with both rotational and reflection symmetry.
Answer
Make several designs, then test each one twice — once by folding and once by turning — and put it in the right group.
How to sort a design:
Fold test. Try folding it side to side, top to bottom, and along the slanting lines. If any fold matches, the design has reflection symmetry.
Turn test. Trace it, pin the centre and turn. If it matches before a full turn is over, the design has rotational symmetry.
Put it in a group using the two answers.
The pinwheel only turns; the isosceles triangle only folds; the square does both.
Sample answer: Only rotational symmetry: my pinwheel square from the Let Us Think activity; a design of 3 leaves all curving the same way round a centre. Only reflection symmetry: a triangle with a square below it, like a small house; a butterfly cut-out. Both: a square with a triangle on each of its four sides; the four-blue-squares shape above; a plain circle.
What makes the difference: If every arm of your design curls the same way round the centre, you get turning symmetry but no folding line — folding would reverse the curl. If your arms are straight and evenly placed, you get both kinds.