Construct Parallel Lines

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High School Math based on the topics required for the Regents Exam conducted by NYSED.

The following diagram shows how to construct a parallel line through a given point. Scroll down the page for more examples and solutions.
Construct Parallel Lines

How to Construct a Parallel Line Through a Given Point?
Constructing parallel lines with a compass and straightedge uses the converse of the parallel lines theorem. Creating congruent corresponding angles (or congruent AIA or AEA) guarantees parallel lines.
Step 1: Draw a transversal through the given point to intersect the given line.
Step 2: Duplicate an angle created by the transversal and the given line.

Constructing Parallel Lines
Using compass and straightedge to construct parallel lines

Construct Parallel Lines
Construct parallel lines using compass and straightedge, given a line and a point not on that line.

Constructing parallel lines

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