“Perpendicular Lines”

by

Christopher R. Whitworth

Given one line, how can you successfully create another line that is perpendicular to the specified straight line?

Creating two circles on the line whose midpoints intersect the line is the first step in creating a line that is perpendicular to the given line.  The circles must also intersect each other.  Then, place a point at the two intersections of the two circles. Also note that the circles do NOT have to be the same size.

Next, create a line that passes through both points where the two circles intersect.  This will create a line that is perpendicular to your original line.

Next, focus only on the red and blue lines.  Note that they are perpendicular to each other.

You can check to see if the two lines are indeed perpendicular by simply measuring each of the four angles created by the two lines.  If all four angles are measured at 90 degrees, then the two lines are definitely perpendicular.  But first, you must place two points on each line and one point where the two intersect to measure the four angles.  The next step is to measure the four angles, either with Geometers Sketchpad 4.0 or with a protractor.  Then, label each point so that you can name the angles.

As you can see, the four angles do indeed equal 90 degrees each.  This information verifies that the red and blue lines are perpendicular.

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