NCERT Solutions for Class 5th Maths Chapter 10 Prem and Manu cut letters for Lali's birthday wall — Alphabet Cutout
Book page 136 Updated on2026-09-19
Q1.
The letter A has a vertical line of symmetry. So, to cut out the letter ‘A’ — 1. Fold a paper in half. 2. Draw half of the letter A along the fold. 3. Cut along the outline. 4. Open the paper to see the full letter A.
Answer
You only have to draw half of the A. The fold makes the other half for you.
First look at the letter A. It has one line of symmetry — a line standing straight up through the middle. A line of symmetry is a folding line. Fold along it and the two halves sit exactly on each other.
Fold, draw half, cut, open. The fold line becomes the middle of the letter A.
Do it like this:
Fold a paper in half. Press the fold flat so you can see it clearly.
Draw half of the letter A along the fold. Keep the tip of the A on the fold. Draw only one slanting leg and half of the crossbar.
Cut along the outline. Cut through both layers of the paper together. Do not cut the fold itself.
Open the paper. The full letter A is ready.
Why it happens: When the paper is folded, the two layers lie exactly on each other. Whatever you cut on the top layer is cut the same way on the bottom layer. So the second half comes out as the mirror image of the first half — and that is exactly what a line of symmetry means.
Check it yourself: Open your cut-out A and fold it back along the same line. The two halves should cover each other with nothing sticking out. If they do, your A is symmetrical.
Q2.
The letter H has two lines of symmetry. 1. Fold the paper into one-fourth (once vertically, once horizontally). 2. Draw one-fourth of the letter H along the fold. 3. Cut along the outline. 4. Open the paper to see the full letter H.
Answer
For H you draw only one-fourth of the letter. H has two lines of symmetry, so two folds do the rest of the work.
The two lines of H are: one standing up (vertical) and one lying flat (horizontal). Fold along both and the paper becomes one-fourth of its size.
One-fourth of H looks like a small L. Two folds turn that L into a full H.
Do it like this:
Fold the paper into one-fourth. Fold it once up-and-down, then fold it once side-to-side. Now the paper has two folded edges.
Draw one-fourth of the letter H along the folds. It looks like a small letter L touching both folded edges.
Cut along the outline. Cut all four layers together.
Open the paper. The full letter H is ready.
Why it happens: The first fold copies your drawing once. The second fold copies it again. One drawing → two copies → four copies. That is why one-fourth of the letter is enough.
Tip: This only works when the letter really has two lines of symmetry. Try it with the letter G and you will get a strange shape, because G has no line of symmetry at all.
Q3.
Which of the following alphabet cutouts can be made by just drawing half (1/2) or quarter (1/4) of the letter? You can do it by drawing lines of symmetry on the letters. E N X T K V O
Answer
Half (1/2) is enough for E, T, K, V, X and O. Quarter (1/4) is enough for X and O. N cannot be made this way — it has no line of symmetry.
The rule is short:
The letter has one line of symmetry → draw half the letter on one fold.
The letter has two lines of symmetry → draw one-fourth of the letter on two folds.
The letter has no line of symmetry → you must draw the whole letter.
N has no dashed line, so N has to be drawn fully. X and O have two lines each.
E → 1 line (flat) → draw half N → 0 lines → draw the whole letter X → 2 lines → draw a quarter T → 1 line (upright) → draw half K → 1 line (flat) → draw half V → 1 line (upright) → draw half O → 2 lines → draw a quarter
Why N is different: N does look the same when you turn it half a turn, but turning is not folding. There is no line along which N folds onto itself. So the folding trick fails for N.
Q4.
Which of the letters have a horizontal line of symmetry? _________________
Answer
E, K, X and O.
A horizontal line of symmetry lies flat, straight across the letter. Fold the letter along it and the top half must land exactly on the bottom half.
E, K, X and O each fold neatly along a flat line.
Why: In E, the top arm and the bottom arm are the same, and the middle arm sits on the fold. In K, the upper slanting arm and the lower slanting arm are the same. In X the four arms are alike. O is a smooth oval, the same above and below.
Watch out: T and V do not have a flat folding line. Fold T across the middle and the crossbar has nothing to land on.
Q5.
Which of the letters have a vertical line of symmetry? ____________________
Answer
T, V, X and O.
A vertical line of symmetry stands straight up. Fold the letter along it and the left half must land exactly on the right half.
T, V, X and O each fold neatly along an upright line.
Why: T has a crossbar the same length on both sides and a stem right in the middle. V has two slanting arms that mirror each other. X and O are the same on the left and on the right.
Did you notice? The letter A also has a vertical line of symmetry — that is how Prem cut it at the start of the chapter. A is just not in this list of seven letters.
Q6.
Which letters have both vertical and horizontal lines of symmetry? ________
Answer
X and O.
These two letters pass both folding tests.
Fold side to side. X folds onto itself. O folds onto itself.
Fold top to bottom. X folds onto itself again. O folds onto itself again.
So each of them has two lines of symmetry.
Because they have two lines of symmetry, one-fourth of the letter is enough to cut them.
Try This: Fold a paper into one-fourth and draw just a quarter of the letter O — a small curve. Cut and open it. A perfect O comes out.
Why it matters: More lines of symmetry means less drawing. One line → draw half. Two lines → draw a quarter. That is the whole idea of the Alphabet Cutout activity.