Construct Parallel Lines

There is a useful property to show that 2 given lines are parallel. This property states that if 2 given lines are both perpendicular to a third line, then the 2 lines are parallel. The figure below illustrates this property.

Example:

Since AB and PQ are both perpendicular to ST, these 2 lines are parallel.

This property can be used to construct two parallel lines.

Example:

Construct a line parallel to AB and 2 cm above it.

Solution:

Step 1 : Mark a point C anywhere on the line AB. Construct a line perpendicular to AB and passing through C.

Step 2 : Construct a line segment on the perpendicular line 2 cm above C. Label the point as D. Then, construct a line perpendicular to CD and passing through D. This line is parallel to AB.

The following video shows how to construct parallel lines using compass and straightedge, given a line and a point not on that line.

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