Identifying Tessellations worksheet - Free Printable

Let's solve this tessellation worksheet step by step.

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🔷 What is a Tessellation?

A tessellation is a pattern made with identical shapes that:
- Fit together perfectly,
- Have no gaps between them,
- Have no overlapping.

Common examples include squares, triangles, and hexagons.

Now let’s evaluate each shape:

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✔ a. Parallelogram (Rhombus)

- This is a quadrilateral with opposite sides parallel.
- Yes, parallelograms can tessellate.
- They can be arranged edge-to-edge without gaps or overlaps.
> ✔ Answer: YES

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✘ b. Circle

- Circles have curved edges.
- When you place circles next to each other, there are gaps between them.
- You cannot fill a plane completely with circles without gaps.
> ✘ Answer: NO

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✘ c. Star (5-pointed star)

- A regular 5-pointed star has angles that don’t divide evenly into 360°.
- When trying to fit stars together, there will be gaps or overlaps.
- Most stars do not tessellate unless specially designed.
> ✘ Answer: NO

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✔ d. Two Triangles Forming an "X" Shape (Hourglass-like)

- This shape looks like two triangles joined at the tips.
- It's essentially a kite-shaped figure or a diamond with symmetry.
- But more importantly, it's a polygon with straight sides.
- If we consider how it fits: this shape can be repeated to fill space without gaps.
- Think of it as a variation of a rhombus or two equilateral triangles.
> ✔ Answer: YES

*(Note: Even though it looks like two triangles, if they're rigidly connected, it can still tessellate if its angles allow for 360° around a point.)*

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✔ e. Arrow Shape (Chevron or "Banner")

- This is a quadrilateral with two parallel sides and angled ends.
- Shapes like this can tessellate — think of brick patterns or arrow patterns.
- The angles allow them to interlock without gaps.
> ✔ Answer: YES

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✘ f. Rounded Rectangle (Rectangle with Rounded Corners)

- The curved edges make it impossible to fit tightly without leaving gaps.
- Curves don’t align perfectly when repeated.
> ✘ Answer: NO

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✔ g. Zigzag or Lightning Bolt Shape

- This is a polygon with straight sides.
- Even irregular polygons can tessellate if their angles allow fitting together.
- Many zigzag shapes do tessellate (e.g., in tile designs).
- This one can be repeated in a way that fills space.
> ✔ Answer: YES

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✘ h. U-Shaped Figure (like a cup)

- The curved bottom makes it difficult to fit snugly.
- When placed next to others, there will be gaps.
- Also, the open top prevents tight packing.
> ✘ Answer: NO

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✔ i. T-Shape (like a capital "T")

- This is a polyomino (specifically a tetromino).
- The T-tetromino can tessellate when combined with rotations.
- With careful arrangement, multiple T-shapes can fill the plane without gaps.
> ✔ Answer: YES

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✔ Final Answers:

| Letter | Shape | Can it tessellate? |
|--------|------------------------|--------------------|
| a | Parallelogram | YES |
| b | Circle | NO |
| c | Star | NO |
| d | X-shaped (two triangles)| YES |
| e | Arrow/Banner | YES |
| f | Rounded rectangle | NO |
| g | Zigzag / Lightning bolt| YES |
| h | U-shaped (cup) | NO |
| i | T-shape | YES |

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📝 Summary:

- Shapes with straight edges and angles that add up to 360° around a point tend to tessellate.
- Curved shapes (circles, rounded rectangles) usually cannot tessellate due to gaps.
- Irregular polygons may still tessellate if they can be arranged to fill space.

✔ Correct Answers:
- a: YES
- b: NO
- c: NO
- d: YES
- e: YES
- f: NO
- g: YES
- h: NO
- i: YES

Let me know if you'd like a visual explanation or how to draw the tessellations!