Worksheet on determining the 2D shapes created by slicing 3D shapes, with answers provided.

Problem Overview:

The task involves determining the 2D shape that would be created when a 3D shape is sliced as indicated by the blue lines in each diagram. The goal is to analyze each 3D shape and its slicing plane to identify the resulting 2D cross-section.

Solution Explanation:

#### 1. Cube Sliced Horizontally
- 3D Shape: Cube
- Slicing Plane: Horizontal (parallel to the top face)
- Resulting 2D Shape: Square
- When a cube is sliced horizontally, the cross-section is a square because all faces of a cube are squares.

#### 2. Rectangular Prism Sliced Horizontally
- 3D Shape: Rectangular prism
- Slicing Plane: Horizontal (parallel to the top face)
- Resulting 2D Shape: Rectangle
- A rectangular prism has rectangular faces. Slicing it horizontally results in a rectangle.

#### 3. Rectangular Prism Sliced Diagonally
- 3D Shape: Rectangular prism
- Slicing Plane: Diagonal (slanted across two opposite edges)
- Resulting 2D Shape: Square
- If the slicing plane is diagonal but still parallel to one of the square faces of the prism, the result is a square. This depends on the specific orientation, but the given diagram suggests a square cross-section.

#### 4. Triangular Prism Sliced Parallel to the Base
- 3D Shape: Triangular prism
- Slicing Plane: Parallel to the triangular base
- Resulting 2D Shape: Triangle
- Slicing a triangular prism parallel to its triangular base results in a triangle.

#### 5. Pyramid Sliced Horizontally
- 3D Shape: Pyramid (triangular base)
- Slicing Plane: Horizontal (above the base)
- Resulting 2D Shape: Triangle
- Slicing a pyramid horizontally results in a triangle that is similar to the base but smaller in size.

#### 6. Pyramid Sliced Horizontally Near the Apex
- 3D Shape: Pyramid (triangular base)
- Slicing Plane: Horizontal (closer to the apex)
- Resulting 2D Shape: Triangle
- Similar to the previous case, slicing near the apex still results in a triangle, but it will be even smaller.

#### 7. Rectangular Prism Sliced Vertically
- 3D Shape: Rectangular prism
- Slicing Plane: Vertical (parallel to one of the rectangular faces)
- Resulting 2D Shape: Rectangle
- Slicing a rectangular prism vertically results in a rectangle.

#### 8. Triangular Prism Sliced Parallel to the Lateral Face
- 3D Shape: Triangular prism
- Slicing Plane: Parallel to one of the lateral rectangular faces
- Resulting 2D Shape: Rectangle
- Slicing parallel to a lateral face of a triangular prism results in a rectangle.

#### 9. Pyramid Sliced Horizontally Near the Base
- 3D Shape: Pyramid (triangular base)
- Slicing Plane: Horizontal (near the base)
- Resulting 2D Shape: Square
- If the slicing plane is horizontal and close to the base, and the base is a square, the resulting cross-section will be a square.

Final Answer:

\[
\boxed{
\begin{array}{ccc}
1) \text{Square} & 2) \text{Rectangle} & 3) \text{Square} \\
4) \text{Triangle} & 5) \text{Triangle} & 6) \text{Triangle} \\
7) \text{Rectangle} & 8) \text{Rectangle} & 9) \text{Square} \\
\end{array}
}
\]