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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

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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