https://file.aiquickdraw.com/mathbot/file/1726337645444471zvfwj.jpg

Let's break down the question shown in the image.

### 4) 3-D Shapes on a Rectangular Face
The three shapes shown are:
- Triangular prism
- Pentagonal prism
- Hexagonal prism

The task involves completing some tables and comparing results, which are not visible here. But I can help guide you through the geometric properties of these shapes.

### Cube Problem
In the lower part of the image, a cube is shown with a shaded face (labelled ABEF). Let's tackle each sub-question related to this cube.

**a) How many faces are parallel to the shaded face?**
- The face ABEF is parallel to the face CDHG (opposite face of the cube).
- Therefore, **1 face is parallel** to the shaded face.

**b) How many faces are perpendicular to the shaded face?**
- The shaded face ABEF is perpendicular to four other faces: 
  - ABCD
  - ABGH
  - EFGH
  - EDCF
- Thus, **4 faces are perpendicular** to the shaded face.

**c) Name three pairs of parallel edges.**
- Parallel edges on the cube are those that run in the same direction without meeting. Here are three pairs:
  - AB and EF (top and bottom of the shaded face)
  - AD and EH (vertical edges on the left side)
  - BC and FG (vertical edges on the right side)

**d) Name three pairs of perpendicular edges.**
- Perpendicular edges are those that meet at a 90-degree angle. Three pairs are:
  - AB and AD (meet at vertex A)
  - EF and EH (meet at vertex E)
  - BC and CD (meet at vertex C)

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Would you like to go into more detail on any part of this? Here are five related questions to consider:

1. What are the number of faces, edges, and vertices for a cube?
2. How can we determine which faces of a polyhedron are parallel or perpendicular?
3. What is the relationship between the angles of the edges in a prism?
4. How many total parallel edge pairs exist in a cube?
5. How would you describe the differences in geometric properties between a cube and a triangular prism?

**Tip:** When examining 3D shapes, always consider how each face relates to others in terms of parallelism and perpendicularity. This helps in understanding their spatial properties.

How many faces are parallel or perpendicular to a shaded face on a cube, and name three pairs of parallel and perpendicular edges?

Explore the geometry of cubes and prisms by learning how to identify parallel and perpendicular faces. In this problem, students are tasked with determining how many faces are parallel or perpendicular to a shaded face on a cube and identifying three pairs of parallel and perpendicular edges. Suitable for students in Grades 6-8.

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