Identify which 2D shapes can tessellate in this math worksheet.

Let's solve the problem: "Which of these 2D shapes tessellate?"

🔍 What is a Tessellation?

A tessellation is a pattern of shapes that covers a plane (like a flat surface) with no gaps or overlaps. The shapes must fit together perfectly, edge to edge, using only one type of shape, and they can be rotated, reflected, or translated (moved), but not resized.

---

We are given 9 shapes. We need to determine which ones can tessellate on their own.

Let’s go through each shape one by one:

---

1. Cross Shape (Plus Sign)

✔ Yes – it tessellates.
This shape has straight edges and symmetrical arms. You can place multiple copies next to each other so that the "arms" fit into the "holes" of adjacent crosses. This creates a repeating pattern without gaps or overlaps.

> ✔ Tessellates

---

2. Arrow Shape (Right-pointing arrow)

✘ No – it does not tessellate.
The arrow has an uneven edge (a "notch" on the left side). When you try to fit arrows together, the point and the notch don’t match up well. You'll end up with gaps or overlaps unless you use different orientations in a complex way — but even then, it's hard to cover the plane completely without gaps.

> ✘ Does NOT tessellate

---

3. Rhombus (Diamond Shape)

✔ Yes – it tessellates.
All parallelograms (including rhombuses) tessellate because opposite sides are parallel and equal. You can tile the plane with rhombuses by placing them side by side.

> ✔ Tessellates

---

4. Right Triangle

✔ Yes – it tessellates.
Any triangle can tessellate! Triangles can be arranged in a pattern where three meet at a vertex (or more), and they fill the plane perfectly. For example, two right triangles make a rectangle, and rectangles tessellate.

> ✔ Tessellates

---

5. “E” Shape (with a rectangular cut-out)

✘ No – it does not tessellate.
This shape has an irregular inner edge. While it might seem like it could fit with others, the missing corner and the protruding parts don't allow for a seamless tiling. There will always be gaps or overlaps when trying to repeat this shape.

> ✘ Does NOT tessellate

---

6. Shape with Two Curved Sides (Like a Rounded Rectangle)

✘ No – it does not tessellate.
This shape has curved edges. Since curves don’t align perfectly with straight lines or other curves in a repeating pattern, there will always be gaps between shapes. Only shapes with straight edges can typically tessellate.

> ✘ Does NOT tessellate

---

7. Four-Pointed Star (Star with 4 points)

✘ No – it does not tessellate.
While some stars can tessellate (like certain regular star polygons), this one has sharp points and indentations that don’t match up well with adjacent copies. When repeated, gaps appear between the points and valleys.

> ✘ Does NOT tessellate

---

8. Parallelogram (Slanted Rectangle)

✔ Yes – it tessellates.
Like all parallelograms, this shape can be tiled across a plane. Opposite sides are parallel and equal, so they fit together perfectly.

> ✔ Tessellates

---

9. Lightning Bolt Shape

✘ No – it does not tessellate.
This jagged shape has many sharp angles and asymmetries. It doesn’t have matching edges that can fit together without leaving gaps or overlapping. It’s very difficult to tile the plane with this shape.

> ✘ Does NOT tessellate

---

✔ Final Answer: Which shapes tessellate?

The shapes that tessellate are:

1. Cross shape
2. Rhombus (diamond)
3. Right triangle
4. Parallelogram

---

🟩 Summary Table:

| Shape | Tessellates? |
|------|--------------|
| Cross | ✔ Yes |
| Arrow | ✘ No |
| Rhombus | ✔ Yes |
| Right Triangle | ✔ Yes |
| "E" Shape | ✘ No |
| Rounded Shape | ✘ No |
| Four-Pointed Star | ✘ No |
| Parallelogram | ✔ Yes |
| Lightning Bolt | ✘ No |

---

💡 Tip:

Most regular polygons (equilateral triangle, square, hexagon) tessellate. Also, any triangle or quadrilateral can tessellate. But shapes with curves, irregular notches, or asymmetrical features usually do not.

---

✔ So, the shapes that tessellate are:
- The cross
- The rhombus
- The right triangle
- The parallelogram

You would circle or mark these four shapes as the answer.