Q&A for How to Construct a Perpendicular Line to a Given Line Through Point on the Line

Yes. With either of the methods shown above, you may (but don't have to) draw similar arcs on both sides of the given line. An arc (or arcs) on just one side of the line is sufficient, but drawing them on both sides is a good way to verify the accuracy of the perpendicular line.

Assuming no measuring tool or protractor, this can be done with a compass and straightedge. Label the line AB. From A draw another straight line at any acute angle from AB. Mark off six equal segments on this new line. Label the segments AC, CD, DE, EF, FG and GH. Draw a line from H to B. From line AH draw five lines to AB that are each parallel to HB. (Use a compass or protractor to make these lines parallel to HB.) These parallel lines will intersect AB so as to divide AB into six equal parts.

Use that point as "the given point" in either of the above methods.

Only one line can be drawn perpendicular to a straight line at any given point on that line.

Two ways: (1) Pick a different point on the line, and draw a perpendicular line through that point; (2) Simply draw a line parallel to the first perpendicular line.

See the wikiHow: How to Find the Perpendicular Bisector of Two Points .

If you want to inscribe an equilateral triangle inside a circle, you can do it with a protractor and a drawing compass. Draw a circle with the compass, and note the circle's center. At the center, divide the circle into three 60° angles, and note the three points where the radii meet the circumference. Join those three points with straight lines, and you have drawn an inscribed equilateral triangle.

Actually, the two are identical. They look exactly the same. A perpendicular line passing through a point on another line passes through an infinite number of points off that line.