# Construct Parallel Lines

Related Topics:

More Lessons for Geometry
Math Worksheets
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*.

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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.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.