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Steps to Construct a Parallel Line Through a Point

Now it’s time to take a step further and learn how to construct a parallel through a given point. Make an effort to follow the instructions several times—it’s a good way to practice.

Construction of a Parallel Through Point $P$ (Method 1)

Rule

Instructions for Method 1

1.: You have a line $l$ and a point $P$ not located on line $l$ .
2.: Construct the normal from $P$ to the line $l$ . Draw a line from $P$ to $l$ , and draw it well past $l$ . Call this line $m$ .
3.: Now, construct a normal to $m$ at the point $P$ .
4.: The normal you constructed in the previous item is the line that’s parallel to $l$ through $P$ .

Construction of a parallel through a point 1

Construction of a Parallel Through Point $P$ (Method 2)

Construction of a parallel through a point 2

Rule

Instructions for Method 2

1.: You have a line $l$ and a point $P$ not located on line $l$ .
2.: Construct the normal from $P$ to the line. Give the intersection between the line $l$ and the normal the name $B$ .
3.: Mark a point $A$ on the line $l$ .
4.: Construct a normal at $A$ .
5.: Measure the distance from $P$ to $B$ with your draft compass.
6.: Without changing the distance between the legs of your draft compass, put the point on $A$ and make a small arc that intersects with the normal you constructed from $A$ . Call this intersection $C$ .
7.: Draw the line from $P$ to $C$ with a ruler. This line is the parallel to $l$ through the point $P$ .

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Construction of a Parallel Through Point P (Method 1)

Instructions for Method 1

Construction of a Parallel Through Point P (Method 2)

Instructions for Method 2

Construction of a Parallel Through Point $P$ (Method 1)

Construction of a Parallel Through Point $P$ (Method 2)