Worksheet for identifying cross-sectional shapes of 3D figures.

Problem Description:

The task involves identifying the shapes of cross-sections formed when planes intersect three-dimensional figures. The goal is to determine the shape of each cross-section and circle the correct answer from the provided options.

Solution Approach:

1. Understand the Concept of Cross-Sections:
- A cross-section is the two-dimensional shape obtained by slicing a three-dimensional figure with a plane.
- The shape of the cross-section depends on the orientation of the plane relative to the 3D figure.

2. Analyze Each Figure:
- For each 3D figure, identify the plane of intersection and determine the resulting 2D shape.
- Use geometric reasoning to deduce the shape of the cross-section.

3. Match the Shape with the Options:
- Circle the correct shape from the given options for each cross-section.

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Step-by-Step Analysis:

#### Row 1:
1. Figure: A rectangular prism with a horizontal plane cutting through it.
- Analysis: The plane is parallel to the top and bottom faces of the prism.
- Resulting Shape: A rectangle.
- Correct Answer: Circle the rectangle (square-like shape).

2. Figure: A triangular pyramid with a horizontal plane cutting through it.
- Analysis: The plane is parallel to the base of the pyramid.
- Resulting Shape: A triangle.
- Correct Answer: Circle the triangle.

3. Figure: A cylinder with a horizontal plane cutting through it.
- Analysis: The plane is parallel to the circular bases of the cylinder.
- Resulting Shape: A circle.
- Correct Answer: Circle the circle.

4. Figure: A cone with a horizontal plane cutting through it.
- Analysis: The plane is parallel to the circular base of the cone.
- Resulting Shape: A circle.
- Correct Answer: Circle the circle.

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#### Row 2:
1. Figure: A triangular pyramid with a vertical plane cutting through it.
- Analysis: The plane intersects the pyramid along its height, passing through the apex.
- Resulting Shape: A triangle.
- Correct Answer: Circle the triangle.

2. Figure: A square pyramid with a horizontal plane cutting through it.
- Analysis: The plane is parallel to the base of the pyramid.
- Resulting Shape: A square.
- Correct Answer: Circle the square.

3. Figure: A triangular prism with a diagonal plane cutting through it.
- Analysis: The plane intersects the prism diagonally, creating a quadrilateral.
- Resulting Shape: A parallelogram or rhombus (depending on the exact angle).
- Correct Answer: Circle the parallelogram or rhombus (whichever is provided).

4. Figure: A cube with a diagonal plane cutting through it.
- Analysis: The plane intersects the cube diagonally, creating a hexagon.
- Resulting Shape: A hexagon.
- Correct Answer: Circle the hexagon.

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#### Row 3:
1. Figure: A triangular prism with a vertical plane cutting through it.
- Analysis: The plane intersects the prism vertically, passing through two triangular faces.
- Resulting Shape: A rectangle.
- Correct Answer: Circle the rectangle.

2. Figure: A rectangular prism with a diagonal plane cutting through it.
- Analysis: The plane intersects the prism diagonally, creating a parallelogram.
- Resulting Shape: A parallelogram.
- Correct Answer: Circle the parallelogram.

3. Figure: A triangular pyramid with a vertical plane cutting through it.
- Analysis: The plane intersects the pyramid vertically, passing through the apex.
- Resulting Shape: A triangle.
- Correct Answer: Circle the triangle.

4. Figure: A cylinder with a vertical plane cutting through it.
- Analysis: The plane is perpendicular to the circular bases of the cylinder.
- Resulting Shape: A rectangle.
- Correct Answer: Circle the rectangle.

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Final Answer:

Circle the shapes as follows:
1. Row 1: Rectangle, Triangle, Circle, Circle
2. Row 2: Triangle, Square, Parallelogram/Rhombus, Hexagon
3. Row 3: Rectangle, Parallelogram, Triangle, Rectangle

$$
\boxed{\text{See the circled shapes above.}}
$$