Educational tessellation worksheet for learning geometric patterns and shape repetition.

To determine which shapes can tessellate, we need to check if they can fit together perfectly without any gaps or overlaps.

Step-by-Step Analysis:

1. Shape a (Parallelogram):
* Imagine sliding this shape sideways or flipping it. The slanted sides match up perfectly with the slanted sides of another identical shape.
* Because the opposite sides are parallel and equal in length, you can repeat this shape forever in rows.
* Result: Yes, it tessellates.

2. Shape b (Circle):
* Try to push circles together. No matter how close you put them, there will always be curved empty spaces (gaps) between them.
* Circles cannot fill a flat surface completely on their own.
* Result: No, it does not tessellate.

3. Shape d (Hourglass / Two Triangles joined at a point):
* This shape has straight edges. If you take one and flip it upside down, the "V" shape of the top fits perfectly into the inverted "V" of the bottom one.
* You can stack these shapes like bricks to cover a surface without leaving any holes.
* Result: Yes, it tessellates.

4. Shape e (Notched Rectangle / Arrow-like shape):
* Look at the "bite" taken out of the left side and the "point" sticking out on the right side.
* If you slide another identical shape next to it, the point of one fits exactly into the bite of the other.
* They lock together like puzzle pieces.
* Result: Yes, it tessellates.

Final Answer:
a. yes
b. no
d. yes
e. yes