Suppose you construct lines L,M, and N so that L is perpendicular to N and M is parallel to N. What can you conclude?
From the given information, we can conclude that L is perpendicular to M as well.
Ok
Additionally, we can conclude that L, M, and N are coplanar, meaning they all lie in the same plane.
If you construct lines L, M, and N such that L is perpendicular to N and M is parallel to N, the following can be concluded:
1. L and M are not perpendicular: Since L is perpendicular to N and M is parallel to N, it means that L and M are not the same line and do not intersect. Therefore, they cannot be perpendicular.
2. L and N are perpendicular: Given that L is perpendicular to N, it means that L intersects N at a right angle. This relationship remains the same regardless of the relationship between M and N.
3. M and N are parallel: Since M is parallel to N, it means that M and N are two distinct lines that do not intersect and are equidistant at all points. This relationship remains the same regardless of the perpendicularity between L and N.
In summary, the conclusion is that L and N are perpendicular, while M and N are parallel.