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To answer this question, we need to identify which regular polygons can tessellate (tile) the plane. A tessellation means that the shapes can cover the entire plane without gaps or overlaps.

### Answer:
The regular polygons that can tessellate the plane are:
1. **Equilateral Triangles**
2. **Squares**
3. **Regular Hexagons**

#### Explanation:
A regular polygon will tessellate the plane if the interior angles of the polygons can combine to form a full 360° at each vertex. Let's see why each of these polygons works:

- **Equilateral Triangle**: Each interior angle of an equilateral triangle is 60°. Six triangles can meet at a point (6 × 60° = 360°), allowing them to form a tessellation.
- **Square**: Each interior angle of a square is 90°. Four squares can meet at a point (4 × 90° = 360°), so squares can also tessellate the plane.
- **Regular Hexagon**: Each interior angle of a regular hexagon is 120°. Three hexagons can meet at a point (3 × 120° = 360°), enabling hexagons to tessellate as well.

No other regular polygons can tessellate the plane because their angles do not evenly divide into 360°. For example, regular pentagons have interior angles of 108°, which do not allow them to meet perfectly without gaps when tiled.

Would you like more details on the properties of tessellations or have any other questions?

### Related Questions
1. Why can only certain regular polygons tessellate the plane?
2. What is the role of symmetry in tessellation patterns?
3. Can irregular polygons tessellate the plane, and if so, how?
4. How does angle sum contribute to the ability to tessellate?
5. Are there any three-dimensional analogs to tessellation?

### Tip
Remember that for a regular polygon to tessellate, its interior angles must be able to sum up to 360° at each vertex.

Which of the regular polygons will tile the plane as a tessellation (be sure to name all of them)? Explain your answer.

Learn which regular polygons can tessellate the plane, with a clear explanation of why only equilateral triangles, squares, and regular hexagons meet the criteria. This problem explores tessellation, interior angles, and geometric properties for students in Grades 7-10.

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