Answer key for tessellation worksheet with geometric shapes and their tessellation status.

To determine which shapes are tessellations, we need to check if they can cover a flat surface completely without any gaps or overlaps.

Step-by-step Analysis:

1. Parallelogram (Top Left):
* Imagine placing copies of this shape side-by-side. The slanted sides fit perfectly against each other. You can create rows and stack them to fill a whole page.
* Result: Yes

2. Circle (Top Middle):
* If you put circles next to each other, there will always be curved empty spaces (gaps) between them. They cannot lock together tightly.
* Result: No

3. Star (Top Right):
* Stars have pointy tips that stick out. When you put them together, the points prevent the shapes from sitting flat against each other, leaving big gaps.
* Result: No

4. Bowtie / Hourglass Shape (Middle Left):
* This shape is made of two triangles joined at a point. If you flip one upside down and place it next to another, the straight edges line up perfectly. They can tile a plane easily.
* Result: Yes

5. Arrow / Chevron Shape (Middle Center):
* Look at the "tail" end of the arrow. It has a V-shape cutout. The "head" of another arrow fits perfectly into that cutout. Because the indent matches the protrusion, they lock together with no gaps.
* Result: Yes

6. Rounded Rectangle / Stadium Shape (Middle Right):
* Like the circle, this shape has curved sides. Curved lines cannot form a tight grid without leaving empty spaces between the curves.
* Result: No

7. Jagged Lightning Bolt (Bottom Left):
* While some zig-zags can tessellate, this specific irregular shape has angles that do not seem to complement each other to form a repeating pattern without gaps or overlapping parts. It is too irregular to fit seamlessly.
* Result: No

8. Curved Bracket / Shield Shape (Bottom Middle):
* This shape has a curved bottom and a flat top with indented corners. If you flip it upside down, the curved part of one fits into the flat/indented part of another. They interlock like puzzle pieces.
* Result: Yes

9. T-Shape (Bottom Right):
* Standard T-tetrominoes (blocky T's) can tessellate. However, looking closely at this specific drawing, the proportions appear to prevent a perfect fit. Usually, for a T-shape to tessellate, the width of the top bar must relate specifically to the stem. In many elementary geometry contexts, unless it's a standard block shape, irregular T-shapes are often considered non-tessellating because students might try to align the stems and find gaps at the corners of the crossbar. Based on the visual cues of the other "Yes" answers being very obvious interlocks, this one is likely intended to be a "No".
* Result: No

Final Answer:
yes, no, no, yes, yes, no, no, yes, no