Question

In a three-dimensional shape, diagonal is a line segment that joins two vertices that do not lie on the ______

Answer 1

Explanation for the given statement.

1. We know that a diagonal connects two non-adjacent vertices while simultaneously passing through the shape's centre.
2. Also, we know that the vertex is a point in any shape where two and more than two lines or edges meet.

For example:

1. In the figure shown, the red-doted line segment $AC$ is not the diagonal of the three-dimensional shape as the line segment $AC$ does not pass through the shape's centre.
2. The blue-doted line segment $AC\text{'}$ is the diagonal of the three-dimensional shape as the line segment $AC\text{'}$ passes through the shape's centre and also the vertex $A$ and vertex $C\text{'}$ are non-adjacent vertices.

Hence, the diagonal of a three-dimensional shape is a line segment that joins two vertices that do not lie on the same face.