Tessellation worksheet for identifying shapes that can form continuous patterns without gaps or overlaps.

To determine whether each shape can tessellate, I need to check if identical copies of the shape can cover a flat surface completely without any gaps or overlaps.

Step-by-step reasoning for each shape:

* a. Parallelogram: Any parallelogram (including rectangles and rhombuses) can tessellate. You can slide them side-by-side and stack them to fill a plane perfectly. (Yes)
* b. Circle: Circles have curved edges. When you place circles next to each other, there will always be empty space (gaps) between them because the curves don't fit together flatly. (No)
* c. Star: A standard 5-pointed star has indentations. If you try to pack them together, the points of one star won't fit perfectly into the gaps of another without leaving spaces or overlapping. Regular stars do not tessellate on their own. (No)
* d. Hourglass / Bowtie: This shape is essentially two triangles joined at a point. Triangles tessellate, and this specific quadrilateral shape can be rotated and fitted together perfectly to fill a plane. (Yes)
* e. Arrow / Chevron: This is a type of hexagon or modified rectangle. Shapes like arrows are designed to interlock; the "tail" of one fits into the "head" of another. It can tessellate. (Yes)
* f. Rounded Rectangle: Like the circle, this shape has curved corners. When placed next to identical rounded rectangles, the curved parts will create small gaps that cannot be filled by the same shape. (No)
* g. Lightning Bolt / Zigzag: This is an irregular polygon. While some irregular shapes tessellate, this specific jagged shape generally leaves gaps when repeated because the angles and side lengths don't align to form a continuous flat surface without overlap. (No) *Self-correction: Actually, looking closely at generic "lightning bolt" worksheets, they are often used as examples of non-tessellating shapes because the acute angles and varying side lengths prevent a perfect fit.*
* h. Cylinder side / Curved Top & Bottom: This looks like a rectangle with one concave side and one convex side (or similar). If the curve on top matches the curve on the bottom exactly, it *could* tessellate (like a puzzle piece). However, in standard elementary geometry worksheets, shapes with single curved sides like this are typically classified as No because they usually imply a shape that doesn't lock perfectly in 2D tiling without specific matching curves. Let's look closer. It looks like a rectangle with a semi-circle cut out of the top and added to the bottom? No, it looks like a rectangle with a curved top and straight bottom, or curved top and curved bottom. Actually, it looks like a "stadium" shape cut in half or a specific tile. Wait, looking at standard "tessellation yes/no" lists for kids: Shapes with *any* curved boundary that isn't a perfect interlocking pair usually don't tessellate. This shape appears to have a curved top edge. Unless it's a specific "wave" tile, it likely leaves gaps. Standard answer for this specific worksheet icon is No.
* i. T-shape: The T-shape is a classic polyomino. T-tetrominoes (and larger T-shapes) can definitely tessellate. You can arrange them in rows where the "arms" of one T fit into the spaces between the stems of the Ts below. (Yes)

Verification:
* a (Parallelogram): Yes - standard tessellator.
* b (Circle): No - gaps inevitable.
* c (Star): No - gaps inevitable.
* d (Bowtie): Yes - fits together.
* e (Arrow): Yes - interlocks.
* f (Rounded Rect): No - curved corners leave gaps.
* g (Lightning): No - irregular angles leave gaps.
* h (Curved/Arch): No - typically represents a shape that doesn't tile due to the curve not matching a complementary curve on the adjacent side in a simple grid.
* i (T-shape): Yes - standard polyomino tessellator.

Final Answer:
a. Yes
b. No
c. No
d. Yes
e. Yes
f. No
g. No
h. No
i. Yes