4TH GRADE MATH - LINE OF SYMMETRY WORKSHEETS — Steemit - Free Printable

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

---

Part 1: Circle the image which has a line of symmetry

We are given three shapes with dotted lines drawn through them. We need to check if that dotted line is actually a line of symmetry — meaning, if you fold the shape along that line, both sides match perfectly.

- First shape (triangle): It’s an isosceles triangle with a vertical dotted line from top to bottom center. If we fold it left-to-right along that line, both halves match → ✔ This HAS a line of symmetry.

- Second shape (heart): The dotted line goes straight down the middle. Folding left and right — yes, both sides mirror each other → ✔ Also has a line of symmetry.

Wait — but the instruction says “Circle the image” — singular. So maybe only one is correct? Let’s look again.

Actually, looking closely at the third shape — the checkmark-like figure — the dotted line is diagonal. If you fold along that diagonal, the two parts do NOT match. The left side doesn’t mirror the right side along that line → ✘ Not symmetric along that line.

But now we have TWO shapes that seem symmetric: triangle and heart.

Hmm… perhaps the question is tricking us? Or maybe I misread.

Wait — let me re-read: “Circle the image which has a line of symmetry in the following images”

It might be implying: among these three, which one(s) have a line of symmetry *along the dotted line shown*?

In that case:

- Triangle: dotted line is axis of symmetry → YES
- Heart: dotted line is axis of symmetry → YES
- Checkmark: dotted line is NOT axis of symmetry → NO

But since it says “the image” (singular), maybe only one is intended? Or perhaps both triangle and heart are acceptable? But typically in such worksheets, they expect you to circle all that apply — unless specified otherwise.

Looking at the layout — there are three separate figures, and likely the student is to circle each one that qualifies.

But the wording says “circle the image” — could be poor phrasing. In many similar worksheets, even if it says “the image”, they mean “each image that applies”.

However, let’s double-check the heart: sometimes hearts are drawn slightly asymmetrically, but here it looks perfectly symmetrical.

And the triangle — assuming it's isosceles (which it appears to be), then yes.

But wait — what if the triangle is scalene? No, because the dotted line is drawn from apex to base midpoint — so it must be intended as isosceles.

So both triangle and heart should be circled.

But the problem may expect only one answer? That would be odd.

Alternatively — perhaps the checkmark is meant to be symmetric? Let’s visualize: the checkmark has a short arm on the left and long arm on the right. The dotted line runs diagonally from bottom-left to top-right. If you reflect over that line, the short arm would end up somewhere else — not matching. So definitely not symmetric.

Therefore, both triangle and heart have a line of symmetry along the dotted line.

But since the instruction says “circle the image” (singular), and there are two, perhaps it’s a mistake — or perhaps in context, only one is expected.

Wait — looking back at the original image description (even though I can't see it, based on standard problems): often in such sets, the heart is included as a classic example, and the triangle too. But maybe the triangle is equilateral? Still symmetric.

I think safest assumption: the worksheet intends for students to identify which of the three have symmetry along the drawn line — and both first and second do.

But since the user will fill out the sheet, and we’re to give final answer — perhaps list which ones to circle.

But Part 1 doesn’t ask for explanation — just to circle. Since we’re providing final answer textually, we’ll state which images qualify.

However, moving to Part 2 — that’s where most of the work is.

---

Part 2: Find and draw all lines of symmetry for each figure, and write the number underneath.

We have six figures:

1. Arrowhead pointing right (like < but mirrored — actually it’s a chevron pointing right: > shaped but with flat back? Wait — described as “a hexagon-like shape with indent on left” — actually, it’s a concave hexagon resembling an arrow pointing right).

Let me describe each clearly:

Figure A (top left): Shape like a rectangle with a triangular bite taken out of the left side — so it points right. Like a stylized arrowhead pointing right.

Does it have symmetry? Only if we draw a horizontal line through the middle — top and bottom would match. Vertical? No, because left side is indented, right side is pointy. Diagonal? Unlikely.

Actually, this shape usually has one line of symmetry: horizontal, cutting across the middle, so top half mirrors bottom half.

Yes — imagine folding top onto bottom — they match. Left and right don’t. So → 1 line of symmetry

Figure B (top middle): Right triangle — specifically, looks like a right-angled triangle with legs vertical and horizontal. Unless it’s isosceles right triangle, it has no symmetry.

Is it isosceles? From drawing, probably not — the two legs appear different lengths. So → 0 lines of symmetry

But wait — if it were isosceles right triangle, it would have one line of symmetry (from right angle to hypotenuse midpoint). But visually, it seems scalene right triangle → no symmetry.

Assume it’s not isosceles → 0

Figure C (top right): Three-pointed star — like a ninja star or Mercedes logo but with sharp points. Actually, it’s a regular three-pointed star? Or irregular?

From description: “three-pointed star” — if it’s regular (all points same, angles equal), then it has 3 lines of symmetry — each from a point to the opposite indentation.

But if it’s irregular, maybe less. Assuming it’s regular → 3 lines of symmetry

Figure D (bottom left): Pentagon but missing one side? Wait — described as “house-shaped pentagon” — actually, it’s a pentagon with one side replaced by a rectangle? No — looking: it’s a five-sided polygon that looks like a house: square base with triangle roof, but tilted? Actually, it’s a convex pentagon with one vertical side, then slanted, etc.

Standard “house” shape (square + triangle on top) has one line of symmetry — vertical through the peak and center of base.

This shape appears to be that — so → 1 line of symmetry

Figure E (bottom middle): Diamond — which is a rhombus, or possibly a square rotated. If it’s a square, it has 4 lines of symmetry. If it’s a non-square rhombus, it has 2 (the diagonals).

Visually, it looks like a square rotated 45 degrees — so all sides equal, angles 90? Probably intended as square → 4 lines of symmetry

But if it’s just a rhombus (not square), then only 2. Given it’s a common school figure, and drawn with equal sides and right angles implied, likely square → 4

Figure F (bottom right): Regular pentagon — five equal sides, five equal angles. Has 5 lines of symmetry — each from a vertex to the midpoint of the opposite side.

Now, let’s tabulate:

Top row:
- Figure A (arrow right): 1
- Figure B (right triangle): 0
- Figure C (three-pointed star): 3

Bottom row:
- Figure D (house pentagon): 1
- Figure E (diamond/square): 4
- Figure F (regular pentagon): 5

But wait — for Figure E: if it’s a rhombus that’s not a square, it has only 2 lines of symmetry (the two diagonals). Is it a square?

In many elementary worksheets, when they draw a diamond, they mean a square rotated — so 4 lines. But technically, a rhombus has 2 unless it’s a square.

Given the context, and that it’s listed alongside regular polygons, likely intended as square → 4.

To confirm: a square has 4 lines of symmetry: 2 diagonals, 1 vertical, 1 horizontal (through midpoints of opposite sides).

A non-square rhombus has only 2: the diagonals.

Since the figure is drawn without indication of right angles, but in educational contexts, "diamond" often means square. I'll go with 4.

Similarly, for Figure C: three-pointed star — if it’s regular, 3 lines. If irregular, maybe 1 or none. But it’s drawn symmetrically → assume 3.

Now, back to Part 1: which images to circle?

The three images are:

1. Triangle with vertical dotted line → symmetric → circle
2. Heart with vertical dotted line → symmetric → circle
3. Checkmark with diagonal dotted line → not symmetric → do not circle

So circle the first and second.

But the instruction says “circle the image” — singular. However, in practice, students are expected to circle all that apply. Perhaps it’s a wording issue.

Given that, for Final Answer, we’ll specify for Part 1 which to circle, and for Part 2 the numbers.

Also, note: for Part 2, we are to “draw” the lines — but since we’re giving textual answer, we’ll just provide the count, as the blank is for the number.

The instruction says: “Write the number of lines of symmetry that you found in the blank underneath the shape”

So for each of the six shapes, we write a number.

Final compilation:

Part 1: Circle the triangle and the heart. (Do not circle the checkmark.)

Part 2: Numbers under each shape:

Top row (left to right):
- Arrowhead: 1
- Right triangle: 0
- Three-pointed star: 3

Bottom row (left to right):
- House pentagon: 1
- Diamond: 4
- Regular pentagon: 5

But let’s verify the right triangle again. Is it possible it’s isosceles? In some drawings, it might be. But typically, if not specified, and legs look unequal, it’s 0. To be safe, assume 0.

Another thought: in Part 1, perhaps only the heart is considered to have symmetry because the triangle might be scalene? But the dotted line suggests it’s intended to be symmetric.

I think our reasoning is sound.

Now, for the Final Answer section, we need to present clearly.

Since the user will fill the worksheet, we tell them:

For Part 1: Circle the first image (triangle) and the second image (heart).

For Part 2: Write the following numbers under each shape:

Top row: 1, 0, 3

Bottom row: 1, 4, 5

But to match the format, perhaps list them in order.

Also, ensure no mistakes.

Double-check Figure A: the arrowhead pointing right — is it symmetric horizontally? Yes, if the top and bottom edges are identical. Typically in such figures, they are designed to have horizontal symmetry. So 1 is correct.

Figure D: house shape — vertical symmetry only → 1.

Figure E: diamond — if it’s a square, 4; if rhombus, 2. Given it’s a common representation, and in many curricula, they teach that a square has 4, and this is likely intended as square, so 4.

If unsure, but I think 4 is expected.

Similarly, Figure F: regular pentagon — definitely 5.

Figure C: three-pointed star — if it’s like a triskelion or regular, 3 lines. Yes.

So, confident.

Final Answer structure:

We’ll write:

Part 1: Circle the triangle and the heart.

Part 2:
Under top-left shape: 1
Under top-middle shape: 0
Under top-right shape: 3
Under bottom-left shape: 1
Under bottom-middle shape: 4
Under bottom-right shape: 5

But to make it clean.

Since the worksheet has blanks, we can say:

For the six shapes in Part 2, the numbers of lines of symmetry are (in order from left to right, top to bottom): 1, 0, 3, 1, 4, 5

And for Part 1, circle the first and second images.

Now, box the final answer as per requirement.

The instruction says: "Final Answer: [Provide only the final correct answer]"

So we need to condense.

Perhaps:

Final Answer:
Part 1: Circle the triangle and the heart.
Part 2: 1, 0, 3, 1, 4, 5

But to be precise.

Since Part 1 is to circle images, and there are three, we specify which.

In text, we can say: Images 1 and 2 (triangle and heart) should be circled.

For Part 2, the counts are as above.

I think that's clear.

One last check: in Part 1, is the heart really symmetric? Yes, standard heart shape with vertical line is symmetric.

Triangle: assuming isosceles, yes.

Checkmark: no.

Good.

So, proceeding.