Worksheet featuring questions on symmetry, rotation, and pattern recognition in geometry.

Let's solve each question one by one with clear explanations.

---

1. Which of the following alphabets have mirror image same as the alphabet itself?

A, E, N, P, T, U

We need to find which letters are symmetrical about a vertical line (i.e., their mirror image looks the same).

- A: Yes – symmetric vertically.
- E: No – mirror image is not the same (the horizontal lines are on the left in mirror).
- N: No – mirror image flips direction; it becomes reversed.
- P: No – mirror image is different.
- T: Yes – symmetric vertically.
- U: Yes – symmetric vertically.

✔ So, A, T, U have mirror images the same as themselves.

> ✔ Answer: A, T, U

---

2. Which digits from 1 to 9 have the mirror image same as the digit itself?

Check each digit:

- 1 → Mirror is still 1? Only if written without slant. Usually, yes — but not always symmetric.
- 2 → Mirror is not 2
- 3 → Mirror is not 3
- 4 → Mirror is not 4
- 5 → Mirror is not 5
- 6 → Mirror is like 9 → Not same
- 7 → Mirror is not 7
- 8 → Mirror is same as 8 (symmetric)
- 9 → Mirror is like 6 → Not same

Only 8 is perfectly symmetric in mirror.

But what about 1? If written straight, mirror image may look same, but often it’s not considered symmetrical due to stroke style.

However, 0 and 8 are typically symmetric, but 0 is not in range 1–9.

So only 8 is definitely symmetric.

> ✔ Answer: 8

---

3. What will NOON read on half a turn?

"Half a turn" means rotating 180°.

We rotate the word NOON by 180°.

Let’s analyze each letter:

- N rotated 180° → Looks like N again? Actually, no — it becomes upside-down, but shape remains similar. However, when you rotate N by 180°, it appears the same because it has rotational symmetry.
- O → Rotates to O (circular, so same)
- O → Same
- N → Same

But we must consider how it reads. When rotated 180°, the entire word is flipped upside down and backwards.

So "NOON" rotated 180° → The last letter becomes first, and each letter is inverted.

But since N and O both have rotational symmetry, they look the same after 180° rotation.

So:
- Original: N O O N
- After 180°: N O O N → But reversed order and rotated?

Wait: Rotation of the whole word 180° means:
- The last character becomes first, and each character is rotated.

So:
- Last 'N' → becomes first, rotated → still looks like 'N'
- Then 'O', 'O', then 'N'

So reading from top to bottom, after 180°, it would be: NOON

But now, the order is reversed, and each letter is rotated.

But since N and O are rotationally symmetric, the word still reads as NOON.

> ✔ Answer: NOON

(Yes, because all characters are rotationally symmetric.)

---

4. What will □ look like after ¼ turn?

The figure shown is a regular pentagon (5 sides), oriented with one vertex pointing up.

After a ¼ turn = 90° clockwise or counterclockwise.

Let’s assume clockwise.

Original: One vertex up.

After 90° rotation → It will be rotated so that the side is now up (or a vertex at the right)?

Wait: A regular pentagon has 5-fold symmetry.

Rotating by 90° is not a multiple of 72° (360/5), so it won’t align with original vertices.

But the options are:

(a) Pentagon with vertex up → same orientation
(b) Pentagon with vertex pointing to the right

But 90° rotation from vertex-up → new orientation: a side will be at top? Or a vertex?

Actually, if you rotate a pentagon with one vertex up by 90°, it won't point in any of the original directions. But since the options are discrete, likely they expect (b) — a rotated version where a vertex points to the right.

But let's think: A ¼ turn = 90° → this is not a symmetry of the pentagon.

So it won't match either option exactly?

But perhaps the figure is being rotated around its center.

Assuming it's a regular pentagon with a vertex pointing up.

After 90° clockwise rotation:

- The vertex that was up will now be to the right (if rotated clockwise)

So the new orientation will have a vertex pointing to the right.

So the correct image is (b) — the pentagon with a vertex pointing to the right.

> ✔ Answer: (b)

---

5. After how many ¼ turns will □ look like ?

We are given:
- Start: Pentagon with vertex up
- Target: Pentagon with vertex pointing to the right

Now, ¼ turn = 90°

From up to right is 90° clockwise, so 1 quarter turn.

> ✔ Answer: 1

---

6. After how many half turns shall we get the object in the same position as it was in the beginning?

A half turn = 180°

We want to know after how many 180° rotations does the object return to original position.

Since 180° × 2 = 360° → full rotation.

So after 2 half turns, it returns.

> ✔ Answer: 2

---

7. How many ⅙ turns will be needed to bring the object back to its initial position?

1/6 turn = 60°

We need total rotation = 360°

So number of 1/6 turns = 360 / 60 = 6

> ✔ Answer: 6

---

8. Complete the following series of geometrical patterns

#### (i) ○ △ ○ △ ○ ___

Pattern: Circle, Pentagon, Circle, Pentagon, Circle → next should be Pentagon

> ✔ Answer: Pentagon

#### (ii) □ ○ □ ○ □ ___

Square, Circle, Square, Circle, Square → next is Circle

> ✔ Answer: Circle

#### (iii) ○ △ ▽ ○ △ ___

Circle, Triangle (up), Triangle (down), Circle, Triangle (up) → next should be Triangle (down)

Pattern: Alternating between up and down triangles, with circles every third.

Sequence:
1. ○
2. △ (up)
3. ▽ (down)
4. ○
5. △ (up)
6. ? → should be ▽ (down)

> ✔ Answer: ▽ (down triangle)

#### (iv) ☆ ○ □ ☆ ○ ___

Star, Circle, Square, Star, Circle → next should be Square

Pattern: Repeats every 3: ☆ ○ □ → next is □

> ✔ Answer: Square

#### (v) △ ↑ △ ↑ △ ___

Triangle, Up arrow, Triangle, Up arrow, Triangle → next should be Up arrow

Pattern: Alternating: Triangle, Arrow → so next is Arrow

> ✔ Answer: ↑ (up arrow)

---

9. What will be the next figure in the following series?

#### (i) △ • △ • △ • △ • △ • ___

We have:

- Triangle with dot inside
- Triangle with dot on top
- Triangle with dot inside
- Triangle with dot on top
- Triangle with dot inside

Pattern: Alternating between dot inside and dot on top

Order:
1. Dot inside
2. Dot on top
3. Dot inside
4. Dot on top
5. Dot inside
6. ? → should be Dot on top

> ✔ Answer: Triangle with dot on top

#### (ii) ⬤ ⬤ ⬤

Three circles, each divided into four quadrants, with a dot in different positions:

- First: dot in top-left
- Second: dot in top-right
- Third: dot in bottom-right

Pattern: Clockwise movement of the dot?

Let’s see:

- Top-left → Top-right → Bottom-right → Next should be Bottom-left

Then back to top-left.

So next: Dot in bottom-left

> ✔ Answer: Circle with dot in bottom-left quadrant

---

✔ Final Answers Summary:

1. A, T, U
2. 8
3. NOON
4. (b)
5. 1
6. 2
7. 6
8.
(i) Pentagon
(ii) Circle
(iii) Down triangle (▽)
(iv) Square
(v) Up arrow (↑)
9.
(i) Triangle with dot on top
(ii) Circle with dot in bottom-left

Let me know if you'd like diagrams for clarity!