Construct Parallel Lines

In this lesson, we will learn

• how to construct parallel lines.
• how to construct a line parallel to another line and through a given point.

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.

Construct a line parallel to another line and through a given point

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

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.