To construct a perpendicular line through a point on a line, the following steps are commonly included:

1. Mark the given point on the line: Identify and mark the point where the perpendicular line is to be drawn.

2. Place the compass on the point: Use a compass and place its needle on the given point.

3. Draw arcs from the point on both sides of it: Using the compass, draw two arcs from the point, one on each side, intersecting the line at two points.

4. Adjust the compass width: Without changing the compass width, place the needle at one of the intersection points and draw an arc above or below the line.

5. Repeat for the other intersection: Now, place the compass needle on the other intersection and draw another arc above or below the line, creating an intersection point with the previous arc.

6. Draw the perpendicular line: Use a straightedge to connect the given point to the point where the arcs intersect. This line will be perpendicular to the original line.

Do you want further details on any of these steps?

Here are 5 related questions:

1. What is the difference between constructing a perpendicular and a parallel line?
2. How can you verify that a line is truly perpendicular using a protractor?
3. What are alternative methods for constructing a perpendicular line without a compass?
4. Can perpendicular lines be constructed in three-dimensional space? How?
5. What real-world applications involve perpendicular line constructions?

Tip: Always ensure your compass width stays constant when drawing intersecting arcs to maintain accuracy in the construction.