Identifying Tessellations worksheet - Free Printable

Problem Overview:

The task is to determine whether each given shape can tessellate. Tessellation refers to the ability of a shape to cover a plane completely without any gaps or overlaps. The goal is to identify which shapes can form such a pattern.

Solution Approach:

To solve this, we need to analyze each shape and determine if it can be repeated in a way that fills the plane without leaving any gaps or causing overlaps. Here’s how we evaluate each shape:

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#### Shape a: Parallelogram
- A parallelogram can tessellate because its opposite sides are parallel and equal in length. By arranging multiple parallelograms side by side, they can fill the plane perfectly.
- Answer: Yes

#### Shape b: Circle
- Circles cannot tessellate because there will always be gaps between them when placed next to each other. No matter how you arrange circles, there will be spaces that cannot be filled by another circle.
- Answer: No

#### Shape c: Star
- A star (specifically a regular star like the one shown) generally cannot tessellate because its points and edges do not fit together seamlessly without gaps or overlaps. Regular stars like pentagrams or heptagrams do not tessellate in a simple pattern.
- Answer: No

#### Shape d: Diamond (Rhombus)
- A rhombus (diamond shape) can tessellate because all its sides are equal, and its angles allow it to fit together with other rhombuses without gaps or overlaps.
- Answer: Yes

#### Shape e: Arrow
- The arrow shape shown here can tessellate. By arranging arrows in a specific pattern, they can fit together seamlessly to cover the plane without gaps or overlaps.
- Answer: Yes

#### Shape f: Oval
- An oval (ellipse) cannot tessellate because, similar to a circle, there will always be gaps between ovals when placed next to each other. Ovals do not have straight edges that can align perfectly to fill the plane.
- Answer: No

#### Shape g: Lightning Bolt
- The lightning bolt shape shown here can tessellate. Its design allows it to fit together with other identical shapes in a repeating pattern without gaps or overlaps.
- Answer: Yes

#### Shape h: Cylinder
- A cylinder is a 3D shape, but the context here seems to refer to its 2D representation (a rectangle with curved ends). Even as a 2D shape, it cannot tessellate because the curved ends do not align properly to fill the plane without gaps.
- Answer: No

#### Shape i: T-shape
- The T-shape can tessellate. By arranging multiple T-shapes in a specific pattern, they can fit together seamlessly to cover the plane without gaps or overlaps.
- Answer: Yes

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Final Answers:

1. a. Parallelogram: Yes
2. b. Circle: No
3. c. Star: No
4. d. Diamond (Rhombus): Yes
5. e. Arrow: Yes
6. f. Oval: No
7. g. Lightning Bolt: Yes
8. h. Cylinder: No
9. i. T-shape: Yes

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Summary:

- Yes: a, d, e, g, i
- No: b, c, f, h

This completes the analysis and solution for the tessellation problem. If you have any further questions, feel free to ask!