Symmetry worksheet asking students to identify lines of symmetry in geometric shapes.

Explanation:
We need to check whether the dotted line shown on each shape is a line of symmetry. A line of symmetry means that if you fold the shape along that line, both sides match exactly — one side is a mirror image of the other.

Let’s go through each shape one by one:

a. Square with vertical dotted line through center → Left and right halves are identical. ✔ Yes
b. Triangle (isosceles) with vertical line through tip and base midpoint → Left and right match. ✔ Yes
c. T-shaped figure with vertical line down the middle → Top bar is symmetric, stem is centered. ✔ Yes
d. Arrow-like shape (pentagon-like) with vertical line → Left and right sides look identical. ✔ Yes
e. Letter “E” with horizontal dotted line through middle → Top and bottom parts of E are not mirror images (top has 3 bars, bottom has 1). ✘ No
f. Rectangle with a triangle cut out on right side, dotted vertical line → Left side is full rectangle, right side has a missing triangle — not symmetric. ✘ No
g. Shape like an M or double peak with vertical line → Left and right sides match perfectly. ✔ Yes
h. Circle with diagonal dotted line → Any line through center of a circle is a line of symmetry. ✔ Yes
i. Trapezoid with horizontal dotted line through middle (parallel to bases) → Top and bottom bases are different lengths; folding wouldn’t match. ✘ No
j. Regular hexagon with diagonal dotted line (from one vertex to opposite) → Regular hexagons have symmetry across diagonals through opposite vertices. ✔ Yes
k. Shape like a house with a notch in the middle bottom, vertical dotted line → Left and right sides are mirror images. ✔ Yes
l. (Note: The last shape is labeled “d.” again — likely a typo; it's a parallelogram tilted, with a diagonal dotted line.) Parallelogram with diagonal line — unless it's a rhombus or rectangle, diagonals are *not* lines of symmetry. This is a generic parallelogram (non-rectangle, non-rhombus), so folding along that diagonal won’t match. ✘ No

Wait — let’s double-check labeling. In the image, there are 12 shapes labeled: a, b, c, d, e, f, g, h, i, j, k, and then another d at the end. That seems like a mislabel — probably meant to be l, but we’ll treat it as the 12th item.

Let me list them clearly with labels as given:

1. a — square → yes
2. b — triangle → yes
3. c — T-shape → yes
4. d — arrow/pentagon → yes
5. e — E with horizontal line → no
6. f — K-like shape (rectangle with triangle cutout) → no
7. g — double peak → yes
8. h — circle → yes
9. i — trapezoid with horizontal line → no
10. j — hexagon with diagonal → yes
11. k — house with notch → yes
12. d (second d) — parallelogram with diagonal → no

So final answers per label:
a: yes
b: yes
c: yes
d: yes
e: no
f: no
g: yes
h: yes
i: no
j: yes
k: yes
d (last): no

But since the worksheet lists two "d"s, and likely the last one was meant to be "l", we’ll answer based on position — the 12th shape is not symmetric.

Now verify tricky ones:

- j: regular hexagon — yes, it has 6 lines of symmetry, including diagonals through opposite vertices. The dotted line goes from one vertex to opposite — correct symmetry. ✔
- i: isosceles trapezoid? No — the dotted line is horizontal (midline), but for symmetry, the line must reflect top to bottom. In an isosceles trapezoid, the *vertical* midline is symmetry, not horizontal. Here the line is horizontal, so top and bottom are different lengths → not symmetric. ✘
- f: looks like a rectangle with a right triangle removed from right side — left side is solid, right side indented → not symmetric. ✘
- l (second d): parallelogram skewed — only rectangles/rhombuses/squares have diagonal symmetry; this is neither → ✘

All checks confirm.

Final 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