Find and extend geometric patterns in this educational worksheet.

Problem Description:

The task involves identifying and extending a geometric pattern. The image shows a series of shapes arranged in rows, with the last shape in each row left blank. The goal is to determine the next shape in the sequence for each row based on the observed pattern.

Solution Approach:

To solve this problem, we need to analyze each row individually and identify the underlying pattern. Once the pattern is understood, we can determine the missing shape that logically extends the sequence.

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Row-by-Row Analysis:

#### Row 1:
- Shapes: Circle, Square, Triangle, Circle, Square, ?
- Pattern: The shapes alternate in a repeating sequence: Circle → Square → Triangle.
- Missing Shape: After "Square," the next shape in the sequence is "Triangle."

#### Row 2:
- Shapes: Rectangle, Diamond, Rectangle, Diamond, Rectangle, ?
- Pattern: The shapes alternate between "Rectangle" and "Diamond."
- Missing Shape: After "Rectangle," the next shape in the sequence is "Diamond."

#### Row 3:
- Shapes: Half-circle (top), Half-circle (bottom), Half-circle (top), Half-circle (bottom), Half-circle (top), ?
- Pattern: The half-circles alternate between being oriented at the top and bottom.
- Missing Shape: After "Half-circle (top)," the next shape in the sequence is "Half-circle (bottom)."

#### Row 4:
- Shapes: Square, Square, Square, Square, Square, ?
- Pattern: All shapes are identical squares.
- Missing Shape: The sequence continues with another "Square."

#### Row 5:
- Shapes: Diamond, Diamond, Diamond, Diamond, Diamond, ?
- Pattern: All shapes are identical diamonds.
- Missing Shape: The sequence continues with another "Diamond."

#### Row 6:
- Shapes: Triangle, Triangle, Triangle, Triangle, Triangle, ?
- Pattern: All shapes are identical triangles.
- Missing Shape: The sequence continues with another "Triangle."

#### Row 7:
- Shapes: Diamond, Square, Triangle, Diamond, Square, ?
- Pattern: The shapes repeat in a cycle: Diamond → Square → Triangle.
- Missing Shape: After "Square," the next shape in the sequence is "Triangle."

#### Row 8:
- Shapes: Diamond, Diamond, Square, Diamond, Diamond, ?
- Pattern: The shapes alternate between two "Diamonds" followed by one "Square."
- Missing Shape: After "Diamond," the next shape in the sequence is "Square."

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Final Answer:

Based on the analysis above, the missing shapes for each row are as follows:

1. Row 1: Triangle
2. Row 2: Diamond
3. Row 3: Half-circle (bottom)
4. Row 4: Square
5. Row 5: Diamond
6. Row 6: Triangle
7. Row 7: Triangle
8. Row 8: Square

Thus, the completed pattern is:

$$
\boxed{\text{Triangle, Diamond, Half-circle (bottom), Square, Diamond, Triangle, Triangle, Square}}
$$