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How to Construct Two Parallel Lines

When you need to construct a line that is parallel to another line, remember that there are always two parallels—the parallel above the line and the parallel below the line.

Constructing Parallels—Method 1

Construction of parallels 1

Rule

Instructions for Method 1

1.
You have a line l, and you want to find a parallel line x cm away.
2.
Mark two points on the line and call them A and B.
3.
Construct 90° angles at both A and B—the normals.
4.
Set the distance between the legs of your draft compass to x cm, put the point of the draft compass on A, and make a small arc across the corresponding normal. Call this intersection D.
5.
Do the same thing at B, but call this intersection C.
6.
Draw a line through C and D. This line is parallel to l.

Constructing Parallels—Method 2

Construction of parallels 2

Rule

Instructions for Method 2

1.
You have a line l, and you want to find a parallel line x cm away.
2.
Mark a point on l and call it A.
3.
Construct a 90° angle at A—a normal.
4.
Set the distance between the legs of your draft compass to x cm, put the point of the draft compass on A, and make a small arc across the normal. Call this intersection D.
5.
Construct a 90° angle at D.
6.
The normal you constructed at D is parallel to l.

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Steps to Construct a Parallel Line Through a Point