NCERT Solutions for Class 5th Maths Chapter 10 The table of letters H, I, X and Y at 1/4, 1/2, 3/4 and full turn — Turning the Letters

Book page 138 Updated on2026-09-19

Q1.

Observe the letters below. Do they look the same when turned? Dots have been marked on the letters to keep track of the orientation of letters. You may also cut out the letters and fix the centre point of the letter by a nail or use a tracing paper to check if the letter looks the same when turned. (Complete the table for H, I, X and Y.)

Original letter	¹⁄₄ turn	¹⁄₂ turn	³⁄₄ turn	Full turn	Rotational symmetry (Yes/No)
					Yes, at ¹⁄₂ turn

The table from the book. The red dot marks the centre the letter is turned about; the small white dots ride round with the letter so you can see where it has got to. The row for H is already filled in.

Answer

Here is the completed table. H, I and X all have rotational symmetry at a 1/2 turn. Y has none.

Original letter	1/4 turn	1/2 turn	3/4 turn	Full turn	Rotational symmetry (Yes/No)
H	lying down, like ⌶ turned	looks the same — H	lying down again	looks the same — H	Yes, at 1/2 turn
I (a straight bar)	lying flat, like —	looks the same — I	lying flat again	looks the same — I	Yes, at 1/2 turn
X	like a +	looks the same — X	like a +	looks the same — X	Yes, at 1/2 turn
Y	arms point left	upside down, arms at the bottom	arms point right	looks the same — Y	No

How to test a letter — do it yourself:

Cut the letter out of paper, or copy it on tracing paper.
Fix its centre with a pin or a nail. The red dot in the book marks this centre.
Turn it a quarter of the way round and compare it with the printed letter.
Keep turning — half, three-quarters, full. Note down each time it matches.
If it matches before the full turn is over, the letter has rotational symmetry.

Why the white dots are drawn: The letter may look the same but it has really moved. The small white dots ride round with the letter and tell you how far it has turned. The shape matching is what counts, not the dot.

Q2.

Letter I — does it look the same after a 1/4 turn, 1/2 turn, 3/4 turn and a full turn? Does it have rotational symmetry (Yes/No)?

Answer

Yes — the letter I has rotational symmetry, at a 1/2 turn. It does not look the same after a 1/4 turn or a 3/4 turn.

Standing up, lying flat, standing up, lying flat. Only the upright ones match the start.

1/4 turn → the bar lies flat → different
1/2 turn → the bar stands up again → same
3/4 turn → the bar lies flat → different
Full turn → back to the start → same
Rotational symmetry: Yes, at 1/2 turn

Why: The letter I is just a straight bar. Its top end and its bottom end look exactly alike. So turning it upside down changes nothing you can see.

Q3.

Letter X — does it look the same after a 1/4 turn, 1/2 turn, 3/4 turn and a full turn? Does it have rotational symmetry (Yes/No)?

Answer

Yes — the letter X has rotational symmetry, at a 1/2 turn. After a 1/4 turn it becomes a plus sign, which is not the same as X.

A quarter turn makes X stand up as a plus sign. A half turn brings the X back.

1/4 turn → looks like + → different
1/2 turn → looks like X → same
3/4 turn → looks like + → different
Full turn → same
Rotational symmetry: Yes, at 1/2 turn

Why not at 1/4 turn? The four arms of X are equally spaced, but they are spaced a half turn apart in pairs. Turning by a quarter turn puts an arm where there was empty space, so the letter now leans a different way.

Did you know? X is the only letter in this table that also has lines of symmetry — an upright one and a flat one. So X has both reflection symmetry and rotational symmetry.

Q4.

Letter Y — does it look the same after a 1/4 turn, 1/2 turn, 3/4 turn and a full turn? Does it have rotational symmetry (Yes/No)?

Answer

No — the letter Y has no rotational symmetry. It matches the start only after a full turn, and a full turn does not count.

The two arms of Y point up at the start. After every part-turn they point somewhere else.

1/4 turn → arms point sideways → different
1/2 turn → arms point down → different
3/4 turn → arms point the other way → different
Full turn → back to the start → same
Rotational symmetry: No

Why: Y has two arms at the top and one long stem at the bottom. The top and the bottom are not alike. So no part-turn can make it look the same.

But Y is not without symmetry: Y has a vertical line of symmetry. Fold it down the middle and the left arm lands on the right arm. So Y has reflection symmetry but no rotational symmetry.

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