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The problem asks to identify the shapes that can form a repeating pattern (also known as tessellation). Tessellation occurs when a shape can be repeated without any gaps or overlaps to cover a surface.

Looking at the shapes:

1. **Square**: A square can tessellate because it can fit together repeatedly without gaps.
2. **Triangle**: An equilateral triangle can also tessellate, as it can fit perfectly with other triangles without gaps.
3. **Hexagon**: A regular hexagon can tessellate as well, fitting together to cover a surface completely.
4. **Pentagon**: A regular pentagon does **not** tessellate by itself. When repeated, it leaves gaps that cannot be filled with more pentagons.

Therefore, the shapes that can form a pattern by repeating are the **square**, **triangle**, and **hexagon**. The pentagon cannot form a tessellating pattern.

Would you like more details on tessellation, or any clarifications?

Here are 5 related questions to explore further:
1. What are the properties of shapes that allow them to tessellate?
2. Can irregular pentagons tessellate, and under what conditions?
3. What is the significance of angle measures in determining tessellation?
4. How do tessellations apply in real-world designs, like architecture or art?
5. Can non-polygonal shapes tessellate, and how?

**Tip**: For a shape to tessellate, the interior angles must add up in a way that allows the shapes to fit together without gaps.

Draw a ring around the shapes that can form a pattern by repeating.

Learn how to identify shapes that can tessellate, forming a repeating pattern. This lesson covers geometry concepts like polygons and tessellation, focusing on squares, triangles, and hexagons. Perfect for students in Grades 4-6.

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