Identify which 2D shapes can tessellate by repeating on their own.

To determine which shapes tessellate, we need to check if each shape can be used to cover a flat surface completely without any gaps or overlaps. This happens when the angles around a meeting point add up to exactly 360 degrees, or if the shape has parallel sides that allow it to slide into place perfectly.

Let's look at each shape one by one:

1. The Cross (Top Left): This shape has four "arms". If you place one cross down, you can fit other crosses into the empty spaces between the arms. The corners of the arms are 90-degree angles. Four of these corners can meet at a single point (90° + 90° + 90° + 90° = 360°), filling the space perfectly.
* Result: Yes, it tessellates.

2. The Arrow (Top Middle): This is a concave hexagon. The "indentation" on the back of the arrow is shaped exactly like the point of the arrow. If you place an arrow pointing right, you can place another arrow pointing left right next to it, fitting the point into the indentation. By repeating this pattern, you can cover the surface.
* Result: Yes, it tessellates.

3. The Rhombus/Diamond (Top Right): Any quadrilateral (a shape with 4 sides) can tessellate. The opposite angles of a rhombus are equal. If you put four rhombuses together, meeting at their corners, the four different angles will sum to 360 degrees.
* Result: Yes, it tessellates.

4. The Triangle (Middle Left): Any triangle can tessellate. If you take a triangle and rotate it 180 degrees, you can fit it against the original to form a parallelogram. Parallelograms tessellate easily. Alternatively, six triangles can meet at a point if they are equilateral, but even irregular triangles tessellate because their angles sum to 180°, allowing them to fit around a point (180° + 180° = 360°).
* Result: Yes, it tessellates.

5. The "C" or "E" shape (Middle Center): This shape has a rectangular indentation. The indentation is shaped exactly like the protruding part of another identical shape. You can slide one shape into the gap of another.
* Result: Yes, it tessellates.

6. The Shape with Curved Sides (Middle Right): This shape has a straight top and bottom, but curved sides. One side curves in (concave) and the other curves out (convex). The curves are identical. You can fit the "out" curve of one shape perfectly into the "in" curve of the next shape, just like puzzle pieces.
* Result: Yes, it tessellates.

7. The Four-Pointed Star (Bottom Left): This is a concave octagon. The inner corners are 90-degree angles. Four of these inner corners can meet at a point (90° + 90° + 90° + 90° = 360°). The outer points will fit into the spaces created by the arms of neighboring stars.
* Result: Yes, it tessellates.

8. The Parallelogram (Bottom Middle): As mentioned with the rhombus, all quadrilaterals tessellate. A parallelogram is a type of quadrilateral. You can slide copies of it next to each other to form rows, and stack the rows to cover the plane.
* Result: Yes, it tessellates.

9. The Lightning Bolt (Bottom Right): This is a stepped shape. The steps on one side are identical to the steps on the other side (just inverted). You can slide one bolt next to another so the steps interlock perfectly, leaving no gaps.
* Result: Yes, it tessellates.

Conclusion:
Every single shape on this sheet is designed to tessellate. They all have complementary sides or angles that allow them to fit together perfectly.

Final Answer:
All of the shapes tessellate.