Symmetry worksheet2 | PDF - Free Printable

Let’s go step by step to solve this worksheet.

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Part 1: Which letters have lines of symmetry?

We need to check each letter from A to Z (as shown) for line symmetry — meaning, if you draw a line through the letter (vertical or horizontal), one side is a mirror image of the other.

Also, we’re asked to note if rotational symmetry exists — that means if you rotate the letter 180°, it looks the same.

But the main task says:
> Draw lines of symmetry... Write “YES” or “NO” under each letter if rotational symmetry exist.

Wait — let’s read carefully:

The instruction says:
> Which letters of the alphabet have lines of symmetry? Draw lines of symmetry through the letters below to show if line symmetry exist. Write “YES” or “NO” under each of the letters below if rotational symmetry exist.

So two things:
1. For line symmetry: You are supposed to *draw* lines (but since we can’t draw here, we’ll list which ones have it).
2. For rotational symmetry: Write YES or NO under each letter.

BUT — looking at the layout, there’s space under each letter to write YES/NO — and the instruction says “if rotational symmetry exist”. So probably, the YES/NO is only for rotational symmetry.

However, the first sentence asks about line symmetry too. Since we can’t draw, I’ll explain both clearly.

Let’s go letter by letter.

We’ll consider standard block capital letters as shown in the image (sans-serif, bold).

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#### Line Symmetry (Mirror Symmetry):

A letter has vertical line symmetry if you can draw a vertical line down the middle and left/right match.

It has horizontal line symmetry if you can draw a horizontal line across the middle and top/bottom match.

Some have both.

Let’s list:

- A: Vertical yes, Horizontal no → Has line symmetry
- B: Vertical no, Horizontal yes → Has line symmetry
- C: Vertical no, Horizontal yes → Has line symmetry
- D: Vertical no, Horizontal yes → Has line symmetry
- E: Vertical no, Horizontal yes → Has line symmetry
- F: No line symmetry
- G: No
- H: Vertical yes, Horizontal yes → Has line symmetry
- I: Vertical yes, Horizontal yes → Has line symmetry
- J: No
- K: Vertical no, Horizontal no? Wait — actually, K usually doesn’t have perfect line symmetry unless stylized. In most fonts, K has no line symmetry.
- L: No
- M: Vertical yes → Has line symmetry
- N: No (unless rotated, but not mirrored)
- O: Both → Has line symmetry
- P: No
- Q: No
- R: No
- S: No line symmetry, but has rotational symmetry!
- T: Vertical yes → Has line symmetry
- U: Vertical yes → Has line symmetry
- V: Vertical yes → Has line symmetry
- W: Vertical yes → Has line symmetry
- X: Both → Has line symmetry
- Y: Vertical yes → Has line symmetry
- Z: No line symmetry, but has rotational symmetry!

Wait — the worksheet shows letters up to Z, but skips some? Let me check the image description again.

Actually, the user provided an image with these letters arranged:

Row 1: A B C D E
Row 2: F G H I J
Row 3: K L M N O
Row 4: P R S T U ← wait, missing Q? Probably typo or skipped. But in the image, it's written as "P R S T U" — maybe Q is omitted? Or perhaps it's a mistake. Looking back: the user wrote:

“P R S T U” — so likely Q is missing. Then next row: W Z — so V, X, Y are also missing? That seems odd.

Wait — re-examining the original problem text:

The user pasted:

```
A B C D E
F G H I J
K L M N O
P R S T U
W Z
```

That’s incomplete. Missing Q, V, X, Y.

But in the actual image (which we can't see, but based on common worksheets), it’s likely all 26 letters are present. However, the user’s text representation may be truncated.

Looking again at the user’s input:

They wrote:

> A B C D E
> F G H I J
> K L M N O
> P R S T U
> W Z

This suggests that after P comes R (skipping Q?), then S,T,U, then W,Z — skipping V,X,Y.

That must be a formatting error. Probably, it should be:

Row 4: P Q R S T
Row 5: U V W X Y Z

But they wrote “P R S T U” and then “W Z”.

Alternatively, maybe it’s:

After O: P, Q, R, S, T, U — but they skipped Q in typing? Unlikely.

Wait — look at the last part: “Write at least one word...” and there’s a cartoon dog. The letters listed end with W and Z — so perhaps V, X, Y are missing? That would be strange.

Another possibility: the worksheet only includes certain letters? But that doesn’t make sense for “alphabet”.

Perhaps it’s a copy-paste error. To be safe, I’ll assume the full alphabet A-Z is intended, even if not all are listed in the text. Because otherwise, the task is incomplete.

But let’s stick strictly to what’s written in the user’s message.

User wrote:

Letters given:

Row 1: A,B,C,D,E
Row 2: F,G,H,I,J
Row 3: K,L,M,N,O
Row 4: P,R,S,T,U ← note: no Q
Row 5: W,Z ← missing V,X,Y

So total letters: A-O (15), plus P,R,S,T,U (5 more = 20), plus W,Z (2 more = 22). Missing Q,V,X,Y.

That’s 22 letters. Maybe it’s intentional? Or a mistake.

Given that, I’ll work with the letters explicitly listed: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,W,Z

Now, for each, determine:

1. Does it have line symmetry? (We won’t draw, but we can say yes/no)
2. Does it have rotational symmetry? (Write YES or NO under each)

Rotational symmetry (180° rotation): the letter looks the same when turned upside down.

Which letters have rotational symmetry?

Standard answer: H, I, N, O, S, X, Z

Sometimes others depending on font, but in block capitals:

- H: yes
- I: yes
- N: yes (if symmetric, like in sans-serif)
- O: yes
- S: yes
- X: yes
- Z: yes

Others? Let’s check:

- A: no
- B: no
- C: no
- D: no
- E: no
- F: no
- G: no
- J: no
- K: no
- L: no
- M: no
- P: no
- Q: no (not listed anyway)
- R: no
- T: no
- U: no
- V: no (not listed)
- W: no
- Y: no (not listed)

So among the listed letters:

List: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,W,Z

Rotational symmetry YES for: H, I, N, O, S, Z

What about W? If you rotate W 180°, it becomes M — not the same, so no.

U? Rotated becomes n-like shape — no.

T? No.

So only: H, I, N, O, S, Z

Now, for line symmetry — though the instruction says to draw lines, since we can’t, and the YES/NO is specified for rotational symmetry, I think the primary output expected is the YES/NO for rotational symmetry under each letter.

Additionally, the worksheet has two writing tasks at the bottom:

> Write at least one word, name, or phrase that has reflective symmetry when written horizontally.

> Write at least one word, name, or phrase that has reflective symmetry when written vertically.

Reflective symmetry horizontally means: if you write the word and put a mirror above or below it, it matches — i.e., the word reads the same upside down? No.

Clarify:

- Horizontal reflective symmetry: mirror line is horizontal → top and bottom are mirrors. So for a word, each letter must have horizontal symmetry, and the whole word must be symmetric top-bottom.

But typically, for words, we consider the entire word’s appearance.

Easier examples:

For horizontal line symmetry (mirror across horizontal axis): the word should look the same when flipped over a horizontal line. That means each letter must have horizontal symmetry, and the sequence must be palindromic in terms of shape? Actually, it’s tricky.

Common example: "OXIDE" — but let's think.

Actually, for horizontal symmetry, letters like B, C, D, E, H, I, K, O, X are candidates, but the whole word must be symmetric.

Simplest: "HI" — H has both symmetries, I has both. If you flip "HI" over horizontal axis, H stays H, I stays I, so yes.

Similarly, "IO", "OH", etc.

But better: "BOOK" — B has horizontal symmetry, O has both, O has both, K? K does not have horizontal symmetry. So no.

"CHOICE" — C has horizontal, H has, O has, I has, C has, E has — but the order: when flipped horizontally, the word reverses? No.

Important: When reflecting over a horizontal line, the top becomes bottom, but the left-right order remains the same. So for a word to have horizontal reflective symmetry, each letter must individually have horizontal symmetry, and the word doesn't need to be reversed because the reflection doesn't reverse left-right; it reverses top-bottom.

Is that correct?

Example: Take the word "BED". Reflect over horizontal line: B becomes something like a backwards B? No.

Actually, in typography, when you reflect a letter over a horizontal axis, it flips upside down.

So for the word to look the same after horizontal reflection, each letter must look the same when flipped upside down, AND the positions must match — but since it's a horizontal flip, the first letter stays first, second stays second, etc., because the flip is vertical direction, not horizontal.

Yes: horizontal line of symmetry means flipping over a horizontal line (like water reflection), so y-coordinates invert, x-coordinates stay. So the word doesn't reverse left-to-right; each letter is flipped vertically.

Therefore, for the word to be unchanged, each letter must be invariant under vertical flip (i.e., have horizontal line symmetry), and since the order doesn't change, any combination of such letters will work, as long as each letter has horizontal symmetry.

Letters with horizontal line symmetry: B, C, D, E, H, I, K, O, X (in some fonts)

In standard block caps:

- B: yes
- C: yes
- D: yes
- E: yes
- H: yes
- I: yes
- K: sometimes, but often no — in many fonts, K does not have horizontal symmetry because the diagonal arms don't match when flipped.
- O: yes
- X: yes

To be safe, use B, C, D, E, H, I, O, X

So a word like "HI" — both letters have horizontal symmetry, and when flipped, still "HI".

Similarly, "IO", "OH", "BOX" — B has, O has, X has — so "BOX" should work.

Check: Flip "BOX" over horizontal line: B becomes B (since symmetric), O becomes O, X becomes X — and the order is still B-O-X, so yes, it looks the same.

Similarly, "DEED" — D has, E has, E has, D has — and order preserved, so yes.

Now for vertical reflective symmetry: mirror line is vertical, so left and right are swapped. This means the word must be a palindrome in terms of letter shapes, but also each letter must have vertical symmetry? Not necessarily — because when you reflect the whole word over a vertical line, the first letter goes to the last position, and is mirrored.

For example, take "MOM": M has vertical symmetry, O has, M has. When reflected over vertical line, the word becomes "MOM" again because it's a palindrome and each letter is symmetric.

But if a letter doesn't have vertical symmetry, its mirror image might not be the same letter.

For instance, "A" has vertical symmetry, so "AA" works.

"B" does not have vertical symmetry — its mirror image is not B, it's like a backwards B, which isn't a standard letter.

So for vertical reflective symmetry of a word, two conditions:

1. The word must be a palindrome (reads same forwards and backwards).
2. Each letter must have vertical line symmetry, so that when mirrored, it still looks like itself.

Letters with vertical line symmetry: A, H, I, M, O, T, U, V, W, X, Y

So a word like "MOM" — M has vertical symmetry, O has, M has, and it's a palindrome — so when reflected over vertical line, it looks the same.

Similarly, "TOT", "WOW", "AHA", "IVI" (if IVI is considered), "OXO", etc.

Now, back to the rotational symmetry part.

For the letters listed: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,W,Z

We need to write YES or NO under each for rotational symmetry.

As established:

Rotational symmetry (180°): H, I, N, O, S, Z → YES

Others: NO

So:

A: NO
B: NO
C: NO
D: NO
E: NO
F: NO
G: NO
H: YES
I: YES
J: NO
K: NO
L: NO
M: NO
N: YES
O: YES
P: NO
R: NO
S: YES
T: NO
U: NO
W: NO
Z: YES

Note: W is listed, and we said NO — correct, because rotating W 180° gives M, not W.

Similarly, U rotated gives something like n, not U.

Now, for the writing parts:

First: Write at least one word, name, or phrase that has reflective symmetry when written horizontally.

As discussed, "BOX" is good — each letter has horizontal symmetry, and the word doesn't change when flipped over horizontal line.

Other options: "HI", "IO", "DEED", "CHOICE" (C,H,O,I,C,E — all have horizontal symmetry? C yes, H yes, O yes, I yes, C yes, E yes — and order preserved, so yes).

But "CHOICE" might be less obvious. Simpler: "HI" or "BOX".

Second: Write at least one word, name, or phrase that has reflective symmetry when written vertically.

As discussed, "MOM" — palindrome and each letter has vertical symmetry.

"WOW", "TOT", "AHA", "OXO", "LEVEL" — L does not have vertical symmetry! L rotated or mirrored is not L.

"LEVEL": L has no vertical symmetry, E has no vertical symmetry (E mirrored horizontally is not E), V has vertical symmetry, E no, L no — so no.

Better: "MOM", "WOW", "TOT", "AHA", "IVI" (if acceptable), "OXO", "TIT", "HIMIH" — too long.

Simplest: "MOM" or "WOW".

Now, to confirm rotational symmetry for the letters:

Double-check S: Rotate S 180° — it looks the same? Yes, in block font, S is symmetric under 180° rotation.

Z: same.

N: in sans-serif, N rotated 180° looks like N? Let's see: N has diagonal from top-left to bottom-right. Rotate 180°, it becomes diagonal from bottom-right to top-left, which is the same as original if the font is symmetric. In many block fonts, N does have rotational symmetry.

Similarly, H, I, O, X — obvious.

So our list is correct.

Now, for the final answer, since the worksheet asks to write YES/NO under each letter for rotational symmetry, and also to provide words for the symmetry phrases.

But the user didn't specify which part to answer — however, the task is to solve the problem, so I should provide all required outputs.

Since ExplainAnswer is false, TeachTopic false, GeneratePractice false, I only need to give Final Answer.

But what exactly is the final answer? The worksheet has multiple parts.

Probably, the main numerical/logical part is the YES/NO for each letter.

And the two written answers.

So in Final Answer, I should list:

- For each letter in the given list, whether rotational symmetry exists (YES/NO)
- One word for horizontal reflective symmetry
- One word for vertical reflective symmetry

Given the letters are presented in rows, I'll list them in order.

Letters in order as per user input:

Row 1: A, B, C, D, E
Row 2: F, G, H, I, J
Row 3: K, L, M, N, O
Row 4: P, R, S, T, U (note: no Q)
Row 5: W, Z

So sequence: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,W,Z

Rotational symmetry:

A: NO
B: NO
C: NO
D: NO
E: NO
F: NO
G: NO
H: YES
I: YES
J: NO
K: NO
L: NO
M: NO
N: YES
O: YES
P: NO
R: NO
S: YES
T: NO
U: NO
W: NO
Z: YES

For the words:

Horizontal reflective symmetry: "BOX" (or "HI", but "BOX" is three letters, clearer)

Vertical reflective symmetry: "MOM"

To be precise, let's choose:

Horizontal: "HI" — simple, both letters have horizontal symmetry.

Vertical: "MOM" — classic example.

Some might argue "HI" when flipped horizontally: H flipped is still H, I flipped is still I, and since it's horizontal flip, the word remains "HI" — yes.

Similarly, "MOM" for vertical: when reflected over vertical line, since it's a palindrome and each letter symmetric, it looks the same.

Perfect.

So Final Answer should include all.

But how to format?

Since it's a worksheet, perhaps list the YES/NO in order, then the two words.

I think that's it.

Final Answer:

Rotational symmetry (YES/NO for each letter in order A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,W,Z):

NO, NO, NO, NO, NO, NO, NO, YES, YES, NO, NO, NO, NO, YES, YES, NO, NO, YES, NO, NO, NO, YES

Word with horizontal reflective symmetry: HI

Word with vertical reflective symmetry: MOM

To make it clear, I'll write it as:

For the letters:
A: NO, B: NO, C: NO, D: NO, E: NO, F: NO, G: NO, H: YES, I: YES, J: NO, K: NO, L: NO, M: NO, N: YES, O: YES, P: NO, R: NO, S: YES, T: NO, U: NO, W: NO, Z: YES

Horizontal symmetry word: HI
Vertical symmetry word: MOM

But since the instruction says "Final Answer: [Provide only the final correct answer]", and it's a bit long, perhaps condense.

Notice that in the worksheet, the YES/NO is to be written under each letter, so listing them in sequence is fine.

I think this is acceptable.

One thing: in row 4, it's P,R,S,T,U — so after P is R, skipping Q. We handled that.

Also, W and Z at the end.

So 22 letters.

Count: A to O is 15, then P,R,S,T,U is 5 (total 20), W,Z is 2 (total 22). Yes.

Our YES/NO list has 22 entries.

Positions:

1.A:NO, 2.B:NO, 3.C:NO, 4.D:NO, 5.E:NO, 6.F:NO, 7.G:NO, 8.H:YES, 9.I:YES, 10.J:NO, 11.K:NO, 12.L:NO, 13.M:NO, 14.N:YES, 15.O:YES, 16.P:NO, 17.R:NO, 18.S:YES, 19.T:NO, 20.U:NO, 21.W:NO, 22.Z:YES

Yes.

Words: HI and MOM.

I think that's complete.