How many different pairs of parallel edges are there on a rectangular solid?
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To find the number of different pairs of parallel edges on a rectangular solid, we need to understand the geometry of a rectangular solid.
A rectangular solid, also known as a rectangular prism, has six faces, twelve edges, and eight vertices.
To determine parallel edges, we need to analyze the orientation of the edges.
Step 1: Visualize a rectangular solid in your mind or refer to a diagram.
Step 2: Identify the edges of the rectangular solid. There are twelve edges, labeled as follows:
- Four edges connecting the top face to the bottom face.
- Four edges connecting the front face to the back face.
- Four edges connecting the left face to the right face.
Step 3: Consider each set of parallel edges. In a rectangular solid, there are three pairs of parallel edges:
- Top and bottom edges: There are four pairs.
- Front and back edges: There are four pairs.
- Left and right edges: There are four pairs.
Step 4: Calculate the total number of different pairs of parallel edges.
To calculate the total, we sum up the number of pairs of parallel edges for each orientation.
Four pairs (top-bottom) + four pairs (front-back) + four pairs (left-right) = 12 pairs
Therefore, a rectangular solid has a total of 12 different pairs of parallel edges.