Symmetry Worksheets - Nóriel Notes - Free Printable

Let's solve this step by step.

We are asked to determine whether the dotted line on each shape is a line of symmetry. A line of symmetry divides a shape into two parts that are mirror images of each other. If you fold the shape along the dotted line, both sides should match perfectly.

We'll go through each shape (a to l) and decide: yes or no.

---

a. Rectangle with vertical dotted line

- The rectangle is divided vertically down the middle.
- Both left and right sides are identical.
✔ Yes

---

b. Triangle (equilateral or isosceles) with vertical dotted line from top to base

- The triangle appears symmetric about the vertical line.
- The left and right sides mirror each other.
✔ Yes

---

c. T-shaped figure with vertical dotted line

- The T-shape has a horizontal top bar and a vertical stem.
- The dotted line goes through the center.
- Left and right sides are identical.
✔ Yes

---

d. Arrow-like shape (pointed up) with vertical dotted line

- It’s a symmetrical arrow pointing up.
- The left and right sides are mirror images.
✔ Yes

---

e. Letter "E" with horizontal dotted line

- The dotted line is horizontal, going through the middle of the E.
- The top and bottom parts are not symmetric — the top has one horizontal bar, the bottom has two.
- The top and bottom don’t match.
✘ No

---

f. Letter "K" with vertical dotted line

- The K has a vertical stem and two diagonal arms.
- The left and right sides are not mirror images — the arms are on the same side.
- Folding along the dotted line won't make the two halves match.
✘ No

---

g. M-shaped figure with vertical dotted line

- The shape looks like an upside-down V with extra lines — it’s symmetric about the center.
- The left and right sides are mirror images.
✔ Yes

---

h. Circle with diagonal dotted line

- A circle has infinite lines of symmetry.
- Any line through the center is a line of symmetry.
- The diagonal line passes through the center.
✔ Yes

---

i. Trapezoid with horizontal dotted line

- This is an isosceles trapezoid (equal non-parallel sides).
- The dotted line is horizontal, cutting across the middle.
- But the top and bottom parts are not mirror images — the top is shorter than the bottom.
- So, folding horizontally won’t make them match.
✘ No

---

j. Hexagon with diagonal dotted line

- This is a regular hexagon.
- A regular hexagon has multiple lines of symmetry.
- The dotted line goes from one vertex to the opposite vertex (diagonal).
- This is indeed a line of symmetry.
✔ Yes

---

k. House-like shape with vertical dotted line

- It looks like a house with a door in the center.
- The dotted line goes through the center.
- The left and right sides appear identical.
- The door is centered, so both sides are symmetric.
✔ Yes

---

l. Rectangle rotated (tilted) with diagonal dotted line

- This is a rectangle rotated at an angle.
- The dotted line is drawn diagonally.
- In a rectangle, only the vertical and horizontal lines through the center are lines of symmetry.
- Diagonal lines are not lines of symmetry unless it's a square.
- This is a rectangle, not a square, so the diagonal does not create mirror images.
✘ No

---

Final Answers:

| Shape | Answer |
|-------|--------|
| a | Yes |
| b | Yes |
| c | Yes |
| d | Yes |
| e | No |
| f | No |
| g | Yes |
| h | Yes |
| i | No |
| j | Yes |
| k | Yes |
| l | No |

---

✔ Summary:
Yes: a, b, c, d, g, h, j, k
No: e, f, i, l

Let me know if you'd like this formatted as a printable answer sheet!