Symmetry worksheet for identifying and drawing lines of symmetry in various shapes.

Let's go through each part of the symmetry worksheet step by step and solve it.

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Part 1: Tell whether the dotted line on each shape represents a line of symmetry. Write yes or no.

We need to determine if the dotted line divides the shape into two mirror-image halves.

#### a.
- Shape: A double-ended arrow-like figure (like a bowtie).
- Dotted line: Vertical line down the middle.
- Analysis: The left and right sides are mirror images.
- ✔ Yes

#### b.
- Shape: A star-like shape with 8 arms (like a snowflake), but rotated.
- Dotted line: Diagonal from top-left to bottom-right.
- Analysis: If you fold along that diagonal, the arms don't match up perfectly — the pattern is not mirrored across that line.
- ✘ No

#### c.
- Shape: A right triangle.
- Dotted line: From the right angle to the opposite vertex (hypotenuse).
- Analysis: This line does not divide the triangle into two congruent parts. Only an isosceles triangle has a line of symmetry from the apex to the base.
- ✘ No

#### d.
- Shape: An arrow pointing up with a rectangle below.
- Dotted line: Horizontal line through the center.
- Analysis: The top (arrowhead) and bottom (rectangle) are not mirror images. The arrowhead is pointy, the bottom is flat.
- ✘ No

> Answers for Part 1:
> - a. Yes
> - b. No
> - c. No
> - d. No

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Part 2: Draw a line of symmetry on each shape.

We are to draw one line of symmetry for each shape.

#### e.
- Shape: A capital "C" or a U-shape with a gap.
- Analysis: It has no vertical symmetry, but it might have horizontal symmetry? Let's see:
- Top and bottom are not symmetric.
- But wait — this shape is like a rectangle with a rectangular piece missing from the middle on the left side.
- Actually, this looks like a U-shaped outline, but open on the left.
- It has no line of symmetry unless it's symmetric about a vertical line?
- Wait — if it's like a rectangle with a rectangular notch on the left side, then it’s not symmetric at all.
- But let’s assume it's a symmetric U-shape, like a horseshoe.
- Then it has vertical symmetry.
- So draw a vertical line down the middle.

✔ Draw a vertical line down the center.

#### f.
- Shape: A clover-like shape (three rounded lobes).
- Analysis: This is a three-leaf clover.
- It has rotational symmetry, but only one line of symmetry — through the center of the top lobe.
- Draw a vertical line through the top lobe.

✔ Draw a vertical line through the center of the top leaf.

#### g.
- Shape: A circle with three lines radiating from the center (like a peace symbol or Mercedes logo).
- Analysis: This has three lines of symmetry, each passing through the center and a "spoke".
- We can draw any one of them.
- For example, draw a vertical line through the top spoke.

✔ Draw a vertical line through the top spoke.

#### h.
- Shape: A rectangle with a small rectangle sticking out from the right side.
- Analysis: Not symmetric horizontally or vertically unless the extension is centered.
- But here, it's only on one side → no symmetry?
- Wait — maybe it's symmetric about a vertical line through the center of the entire shape?
- Let’s imagine: the main rectangle and the extension — if they’re aligned and centered, then yes.
- But since the extension is on the right, it breaks symmetry.
- Actually, this looks like a rectangular shape with a bump on the right.
- That means no line of symmetry?

Wait — look again: it’s a rectangle with a smaller rectangle attached to the right side, centered vertically.

So the whole shape is not symmetric unless we consider reflection.

But if the bump is centered, then there could be vertical symmetry through the center of the entire figure?

Wait — no. The bump is on the right, so the left and right sides are different.

Actually, if the bump is attached to the right side, and the shape is not balanced, then no symmetry.

But perhaps the shape is symmetric about a vertical line through the center of the main rectangle?

No — because the bump is on one side.

Wait — maybe I'm misreading. Let's think:

If the bump is on the right, then the shape is asymmetric.

But perhaps the bump is centered and the overall shape is like a T but sideways?

Wait — actually, the shape looks like a rectangle with a smaller rectangle extending to the right, centered vertically.

That would mean no line of symmetry.

But maybe it's intended to have horizontal symmetry?

No — the bump is on the right, so horizontal symmetry won't help.

Wait — unless the bump is in the center, but the diagram shows it as a projection on the right.

Actually, upon closer inspection, this shape is not symmetric.

But the problem says “draw a line of symmetry” — so it must have one.

Wait — maybe it’s symmetric about a vertical line through the center of the entire shape, meaning the bump is centered?

But in the image, it appears to be a rectangle with a smaller rectangle added to the right, making it asymmetric.

Alternatively, perhaps it's meant to be symmetric about a vertical line through the middle of the large rectangle, but the bump is on both sides?

No — the drawing shows only one bump.

Wait — maybe I’m overthinking.

Looking at standard interpretations: if the bump is only on one side, then no symmetry.

But since the task asks to draw a line of symmetry, it likely does have one.

Alternative idea: Maybe the shape is a rectangle with a central bump, but drawn as a single protrusion.

Wait — no, the diagram shows a rectangle with a smaller rectangle attached to the right side, like a key shape.

This shape has no line of symmetry.

But perhaps it's meant to be symmetric about a horizontal line?

Only if the bump is symmetric top and bottom — which it may be.

Yes! The bump is rectangular, and if it’s attached to the right, but the entire shape is symmetric horizontally?

No — the bump is just a rectangle, so if it’s attached to the right side, and the main shape is tall, then the top and bottom are still symmetric if the bump is centered vertically.

Ah! Yes — if the bump is centered vertically, then the shape has horizontal symmetry.

But wait — the shape is not symmetric about a horizontal line unless the bump is symmetric top/bottom.

But the bump is a rectangle — so yes, it is symmetric top/bottom.

But the whole shape — if the bump is attached to the right side, and the main rectangle is tall, then:

- The top half and bottom half are identical only if the bump is symmetric.

Yes — so if the bump is centered vertically, then the shape has horizontal symmetry.

So draw a horizontal line through the middle.

✔ Draw a horizontal line through the center of the shape.

But wait — looking at the shape: it's a rectangle with a smaller rectangle on the right, and the dotted line is not shown — we are to draw one.

But if the bump is only on one side, then horizontal symmetry is possible only if the bump is symmetric top-to-bottom — which it is.

So yes — the shape has horizontal symmetry.

So draw a horizontal line through the middle.

✔ Horizontal line through the center.

But wait — another possibility: vertical symmetry? Only if the bump were on both sides — but it's not.

So only horizontal.

But let’s reconsider: is the bump centered vertically?

Yes — in such diagrams, unless otherwise specified, we assume it is.

So yes — horizontal symmetry.

✔ Draw a horizontal line through the center.

#### Summary for Part 2:
- e. Draw a vertical line through the center (assuming symmetric U-shape).
- f. Draw a vertical line through the top lobe.
- g. Draw a vertical line through the top spoke (or any spoke).
- h. Draw a horizontal line through the center.

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Part 3: Draw the second half of each symmetrical shape.

We are given the first half of a symmetrical shape, and a dotted line indicating the line of symmetry. We must draw the mirror image of the first half.

#### i.
- Shape: Left half of a heart-like curve.
- Dotted line: Vertical line.
- Action: Reflect the left side across the vertical line to complete the heart.
- ✔ Draw the right half as a mirror image — a smooth curve mirroring the left.

#### j.
- Shape: Left half of a curved shape — like a leaf or spiral.
- Dotted line: Vertical.
- Action: Mirror the left side across the vertical line.
- The shape appears to be a curved shape with a pointed end on the bottom.
- So draw the right half symmetrically — same curvature, mirrored.

#### k.
- Shape: Left half of a polygon — looks like a trapezoid with a notch on the left.
- Dotted line: Vertical.
- Action: Reflect the left half across the vertical line.
- The original has a notch on the left side — so the right side should have a matching notch on the right.
- So draw the right half as a mirror image — same angles and cutout.

#### l.
- Shape: Bottom half of a trapezoid.
- Dotted line: Horizontal.
- Action: Reflect the bottom half across the horizontal line to make a full trapezoid.
- So draw the top half as a mirror image — same width, same slope.

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✔ Final Answers:

#### Part 1: Yes/No
- a. Yes
- b. No
- c. No
- d. No

#### Part 2: Draw a line of symmetry
- e. Vertical line through center (if symmetric)
- f. Vertical line through top lobe
- g. Vertical line through a spoke (e.g., top)
- h. Horizontal line through center

#### Part 3: Draw the second half
- i. Mirror the left half across the vertical line to form a full heart.
- j. Mirror the left half across the vertical line to complete the shape.
- k. Mirror the left half across the vertical line — add the notch on the right.
- l. Mirror the bottom half across the horizontal line to complete the trapezoid.

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📝 Instructions for Drawing:

When drawing:
- Use a ruler for straight lines.
- Ensure mirror symmetry: every point on one side has a matching point at the same distance on the other side.
- Pay attention to curves and angles.

Let me know if you'd like a visual description or sketch instructions for any specific part!