“Parallel Lines”

by

Christopher R. Whitworth

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

The first step in creating a line that is parallel is to create two circles on the line whose midpoints intersect the line.  The circles must also intersect each other.  Then, place a point at each section where the two circles intersect.  Also note that the circles do NOT have to be the same size.

The next step will be to 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.

The next step is to repeat the first step by creating two circles on the perpendicular line.  Remember that they must intersect and must have points placed at each section where the two circles intersect.

The final step is to create a line that passes through both points where the two circles intersect.

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

You can check to see if the two lines are indeed parallel by creating a line that passes through both lines and measuring each of the angles that the lines create.  But first, you must place two additional points on the two parallel lines and at each point where the new line intersects the parallel lines in order to measure the angles.  Then, label each point so that you can name the angles.

Now, you should be able to check to see if the two lines are parallel.  After measuring the angles, if the following data is correct, then the two lines are definitely parallel.

Angle ABC = Angle FBD, Angle HFG, & Angle EFB;

Angle CBD = Angle ABF, Angle EFH, & Angle BFG;

Angle ABF = Angle CBD, Angle EFH, & Angle BFG;

Angle FBD = Angle ABC, Angle HFG, & Angle EFB;

Angle EFB = Angle ABC, Angle FBD, & Angle HFG;

Angle BFG = Angle ABF, Angle CBD, & Angle EFH;

Angle EFH = Angle ABF, Angle CBD, & Angle BFG;

Angle HFG = Angle FBD, Angle ABC, & Angle EFB.

As you can see, the data listed above does indeed match the measurements of the angles above.  The blue and black lines are definitely parallel.

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