Question

in the diagram shown, the distance between points a and c is the same as the distance between points b and g. lines ab and cg are non - coplanar. parallel. perpendicular. skew.

Explanation:

• Non - coplanar: Lines \(AB\) and \(CG\) lie on the same plane (the vertical plane in the diagram), so this option is incorrect.
• Parallel: Parallel lines are coplanar and do not intersect. Lines \(AB\) and \(CG\) are not parallel as they are not in a position where they would never intersect if extended (they are in the same plane and have different directions).
• Perpendicular: Perpendicular lines intersect at a right - angle. There is no indication from the problem statement or the general orientation (based on the coordinate - like axes in the diagram) that they intersect at a right - angle.
• Skew: Skew lines are non - parallel and non - intersecting. But since \(AB\) and \(CG\) are coplanar (in the vertical plane), this is incorrect. However, if we consider the nature of lines in 3 - D space in the context of the diagram (assuming standard 3 - D coordinate - like set - up for planes):
• Lines \(AB\) and \(CG\) are in the same plane (the vertical plane), so non - coplanar is wrong.
• Parallel lines must be in the same direction. \(AB\) is a vertical - like line (assuming the orientation of the axes) and \(CG\) is a horizontal - like line within the vertical plane (so they are not parallel).
• Perpendicular lines: If we assume the \(x - y\) (horizontal - vertical) type of axes in the vertical plane, \(AB\) and \(CG\) are perpendicular.

Answer:

perpendicular.