Which of the following steps is included in the construction of a perpendicular line through a point on a line?

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.

Learn the step-by-step process of constructing a perpendicular line through a point on a line using a compass and straightedge. This guide covers key geometry concepts, including how to use arcs to create perpendicular lines. Suitable for students in Grades 6-8.

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