‘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.
The Correct Answer and Explanation is:
The correct answer is: skew.
Explanation:
To determine the relationship between lines AB and CG, we need to understand their geometric positions in space using the diagram.
Step-by-step Analysis:
- Line AB lies in the vertical plane (let’s call it Plane XZ). Points A and B lie on the same vertical line, so AB is a vertical line.
- Line CG lies in a different vertical plane (Plane YZ), but also appears to be a vertical line because C and G are aligned vertically. However, they lie in a plane that intersects Plane XZ at a right angle (as shown by the small blue square indicating perpendicular planes).
- Both AB and CG are not in the same plane, as they lie on different vertical planes (XZ and YZ respectively), which intersect along the Z-axis.
- Parallel lines lie in the same or parallel planes and never intersect. That is not the case here because these lines lie in perpendicular planes, not parallel ones.
- Perpendicular lines intersect at a right angle. Again, this is not applicable since AB and CG do not intersect at all.
- Coplanar lines lie in the same plane. Since AB and CG lie in different planes, they are non-coplanar.
- Skew lines are lines that do not intersect and are not parallel, and they lie in different planes.
Conclusion:
Lines AB and CG do not intersect, are not parallel, and do not lie in the same plane. Therefore, they are skew lines.
This kind of relationship is common in three-dimensional geometry, where lines can exist in separate planes and have no direct intersection, yet also not be parallel. This concept helps in understanding spatial reasoning and is crucial in fields like architecture, engineering, and 3D modeling.
