How to construct parallel lines using a straight edge and a compass

Step 1:

Draw a line with you straight edge and put one point on the line and label it 1. Then put one point off the line and label it 2.

Step 2:

Connect point 1 and 2 with a straight edge.

Step 3:

Draw an arch at point 1.

Step 4:

Copy that arch at point 2.

Step 5:

Measure the arch at point 1 with your compass.

Step 6:

Then make an arch the distance of point 1's arch at point 2.

Step 7:

Finally, draw a line with your straight edge through point 2 and where the two archs intersect.

This technique requires transferring a measurement. The lines will be only as parallel as the accuracy of the measurement. However, since we can construct a perpendicular line that does not require a measurement, we can construct a parallel line by constructing a perpendicular line to a perpendicular line. The net result is two lines that are parallel by construction. Using two triangles is the same idea--the two lines are parallel by definition.
<p>This is exactly what I thought !</p>
<p>Its geometry, my dear Watson.</p>
<p>Among other things, that's what two triangles are for - drawing parallel lines.</p>
<p>Nicely presented! :)</p>

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More by gun437564:Finding the Distance of a Point to a Line Finding Midpoint of a Line Segment Constructing Perpendicular Lines 
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